Numerical Study of Spin Hall Transport in a Two Dimensional Hole Gas System
Quantum spin liquid emerging in 2D correlated Dirac fermions
“第17届凝聚态理论与统计物理学术会议”日程（初稿）
吴超(西安交通大学) 题目: The influence of local arrangements of oxygen adatoms on the energetics of O2 dissociation over Pt(111) 赵明文(山东大学) 题目: 新型碳材料结构设计和性能调控的理 论模型 李希茂(北京宏剑公司)(12:10-12:25) 题目: 第一原理计算材料的缺陷和掺杂特性
李文飞(南京大学) 题目: 蛋白质分子体系多尺度理论模拟
孙久勋(电子科技大学) 题目: Improvement of unified mobility model and electrical properties for organic diodes under dc and ac conditions
关丽(河北大学)：Structural stability and electronic properties of two nonstoichiometric SrTiO3 phases
休息
报告厅 3（主题: 冷原子物理) 分会报告 ST3.3 主席：成 泽 教授(华中科技大学) (邀请报告) 周琦(香港中文大学) 题目：自旋轨道耦合下波色凝聚体的命运
主席：金国钧 教授(南京大学)
(邀请报告) 杨义峰(中国科学院物理研究所) (邀请报告) 孟胜(中国科学院物理研究所)
题目：重费米子物理中的演生现象
题目：Energy Conversion At Nanoscale
Berry phase
Intrinsic Hall conductivity (Kubo Formula)
Thouless, Kohmoto, Nightingale, den Nijs (1982) Kohmoto (1985)
xy
e2 h
n,k
nF En (k ) Bnz (k )
A (k ): field strength; n : band index Bn (k ) k n
mx x kx
• Ohmic conductivity is dissipative: under T, electric field is even e2 2 J j E j where k F l charge current is odd h (only states close to the Fermi energy contribute!) • Charge supercurrent and Hall current are non-dissipative:
d p ε tr[ μ S F (p) ν S F (p) λ S F (p)]
3 μνλ
1
1
1
• Hall Conductance in terms of momentum space topology
Intrinsic spin Hall effect in p-type semiconductors
Topological Aspects of the Spin Hall Effect
Yong-Shi Wu Dept. of Physics, University of Utah Collaborators: Xiao-Liang Qi and Shou-Cheng Zhang
spin injection and detection
• Spin transport
Spin transport in Cu wires
Outline
• Theory
• Sample fabrication • Measurements
• Switching of ferromagnetic contacts • Spin precession: Hanle effect • Temperature dependence of spin signal
Magnetic impurity scattering due to spin orbit coupling
Transition amplitude to
so so hence H * H
=
so H so
so
p contribute to spin relaxation hence ap
I
Anti-aligned magnetizations
I
I
or
CHANGE IN RESISTANCE BETWEEN ALIGNED AND ANTI-ALIGNED CONFIGURATIONS
Spin Transport in Cu wires
TMR vs Nonlocal Geometry
p s
e
Time scales
Momentum relaxation time Single electron spin coherence time (quantum computing) Electron ensemble spin coherence time (spintronics) Interactions that conserve total spin
卷积神经网络机器学习外文文献翻译中英文2020
卷积神经网络机器学习相关外文翻译中英文2020英文Prediction of composite microstructure stress-strain curves usingconvolutional neural networksCharles Yang，Youngsoo Kim，Seunghwa Ryu，Grace GuAbstractStress-strain curves are an important representation of a material's mechanical properties, from which important properties such as elastic modulus, strength, and toughness, are defined. However, generating stress-strain curves from numerical methods such as finite element method (FEM) is computationally intensive, especially when considering the entire failure path for a material. As a result, it is difficult to perform high throughput computational design of materials with large design spaces, especially when considering mechanical responses beyond the elastic limit. In this work, a combination of principal component analysis (PCA) and convolutional neural networks (CNN) are used to predict the entire stress-strain behavior of binary composites evaluated over the entire failure path, motivated by the significantly faster inference speed of empirical models. We show that PCA transforms the stress-strain curves into an effective latent space by visualizing the eigenbasis of PCA. Despite having a dataset of only 10-27% of possible microstructure configurations, the mean absolute error of the prediction is <10% of therange of values in the dataset, when measuring model performance based on derived material descriptors, such as modulus, strength, and toughness. Our study demonstrates the potential to use machine learning to accelerate material design, characterization, and optimization.Keywords：Machine learning，Convolutional neural networks，Mechanical properties，Microstructure，Computational mechanics IntroductionUnderstanding the relationship between structure and property for materials is a seminal problem in material science, with significant applications for designing next-generation materials. A primary motivating example is designing composite microstructures for load-bearing applications, as composites offer advantageously high specific strength and specific toughness. Recent advancements in additive manufacturing have facilitated the fabrication of complex composite structures, and as a result, a variety of complex designs have been fabricated and tested via 3D-printing methods. While more advanced manufacturing techniques are opening up unprecedented opportunities for advanced materials and novel functionalities, identifying microstructures with desirable properties is a difficult optimization problem.One method of identifying optimal composite designs is by constructing analytical theories. For conventional particulate/fiber-reinforced composites, a variety of homogenizationtheories have been developed to predict the mechanical properties of composites as a function of volume fraction, aspect ratio, and orientation distribution of reinforcements. Because many natural composites, synthesized via self-assembly processes, have relatively periodic and regular structures, their mechanical properties can be predicted if the load transfer mechanism of a representative unit cell and the role of the self-similar hierarchical structure are understood. However, the applicability of analytical theories is limited in quantitatively predicting composite properties beyond the elastic limit in the presence of defects, because such theories rely on the concept of representative volume element (RVE), a statistical representation of material properties, whereas the strength and failure is determined by the weakest defect in the entire sample domain. Numerical modeling based on finite element methods (FEM) can complement analytical methods for predicting inelastic properties such as strength and toughness modulus (referred to as toughness, hereafter) which can only be obtained from full stress-strain curves.However, numerical schemes capable of modeling the initiation and propagation of the curvilinear cracks, such as the crack phase field model, are computationally expensive and time-consuming because a very fine mesh is required to accommodate highly concentrated stress field near crack tip and the rapid variation of damage parameter near diffusive cracksurface. Meanwhile, analytical models require significant human effort and domain expertise and fail to generalize to similar domain problems.In order to identify high-performing composites in the midst of large design spaces within realistic time-frames, we need models that can rapidly describe the mechanical properties of complex systems and be generalized easily to analogous systems. Machine learning offers the benefit of extremely fast inference times and requires only training data to learn relationships between inputs and outputs e.g., composite microstructures and their mechanical properties. Machine learning has already been applied to speed up the optimization of several different physical systems, including graphene kirigami cuts, fine-tuning spin qubit parameters, and probe microscopy tuning. Such models do not require significant human intervention or knowledge, learn relationships efficiently relative to the input design space, and can be generalized to different systems.In this paper, we utilize a combination of principal component analysis (PCA) and convolutional neural networks (CNN) to predict the entire stress-strain c urve of composite failures beyond the elastic limit. Stress-strain curves are chosen as the model's target because t hey are difficult to predict given their high dimensionality. In addition, stress-strain curves are used to derive important material descriptors such as modulus, strength, and toughness. In this sense, predicting stress-straincurves is a more general description of composites properties than any combination of scaler material descriptors. A dataset of 100,000 different composite microstructures and their corresponding stress-strain curves are used to train and evaluate model performance. Due to the high dimensionality of the stress-strain dataset, several dimensionality reduction methods are used, including PCA, featuring a blend of domain understanding and traditional machine learning, to simplify the problem without loss of generality for the model.We will first describe our modeling methodology and the parameters of our finite-element method (FEM) used to generate data. Visualizations of the learned PCA latent space are then presented, a long with model performance results.CNN implementation and trainingA convolutional neural network was trained to predict this lower dimensional representation of the stress vector. The input to the CNN was a binary matrix representing the composite design, with 0's corresponding to soft blocks and 1's corresponding to stiff blocks. PCA was implemented with the open-source Python package scikit-learn, using the default hyperparameters. CNN was implemented using Keras with a TensorFlow backend. The batch size for all experiments was set to 16 and the number of epochs to 30; the Adam optimizer was used to update the CNN weights during backpropagation.A train/test split ratio of 95:5 is used –we justify using a smaller ratio than the standard 80:20 because of a relatively large dataset. With a ratio of 95:5 and a dataset with 100,000 instances, the test set size still has enough data points, roughly several thousands, for its results to generalize. Each column of the target PCA-representation was normalized to have a mean of 0 and a standard deviation of 1 to prevent instable training.Finite element method data generationFEM was used to generate training data for the CNN model. Although initially obtained training data is compute-intensive, it takes much less time to train the CNN model and even less time to make high-throughput inferences over thousands of new, randomly generated composites. The crack phase field solver was based on the hybrid formulation for the quasi-static fracture of elastic solids and implementedin the commercial FEM software ABAQUS with a user-element subroutine (UEL).Visualizing PCAIn order to better understand the role PCA plays in effectively capturing the information contained in stress-strain curves, the principal component representation of stress-strain curves is plotted in 3 dimensions. Specifically, we take the first three principal components, which have a cumulative explained variance ~85%, and plot stress-strain curves in that basis and provide several different angles from which toview the 3D plot. Each point represents a stress-strain curve in the PCA latent space and is colored based on the associated modulus value. it seems that the PCA is able to spread out the curves in the latent space based on modulus values, which suggests that this is a useful latent space for CNN to make predictions in.CNN model design and performanceOur CNN was a fully convolutional neural network i.e. the only dense layer was the output layer. All convolution layers used 16 filters with a stride of 1, with a LeakyReLU activation followed by BatchNormalization. The first 3 Conv blocks did not have 2D MaxPooling, followed by 9 conv blocks which did have a 2D MaxPooling layer, placed after the BatchNormalization layer. A GlobalAveragePooling was used to reduce the dimensionality of the output tensor from the sequential convolution blocks and the final output layer was a Dense layer with 15 nodes, where each node corresponded to a principal component. In total, our model had 26,319 trainable weights.Our architecture was motivated by the recent development and convergence onto fully-convolutional architectures for traditional computer vision applications, where convolutions are empirically observed to be more efficient and stable for learning as opposed to dense layers. In addition, in our previous work, we had shown that CNN's werea capable architecture for learning to predict mechanical properties of 2Dcomposites [30]. The convolution operation is an intuitively good fit forpredicting crack propagation because it is a local operation, allowing it toimplicitly featurize and learn the local spatial effects of crack propagation.After applying PCA transformation to reduce the dimensionality ofthe target variable, CNN is used to predict the PCA representation of thestress-strain curve of a given binary composite design. After training theCNN on a training set, its ability to generalize to composite designs it hasnot seen is evaluated by comparing its predictions on an unseen test set.However, a natural question that emerges i s how to evaluate a model's performance at predicting stress-strain curves in a real-world engineeringcontext. While simple scaler metrics such as mean squared error (MSE)and mean absolute error (MAE) generalize easily to vector targets, it isnot clear how to interpret these aggregate summaries of performance. It isdifficult to use such metrics to ask questions such as “Is this modeand “On average, how poorly will aenough to use in the real world” given prediction be incorrect relative to some given specification”. Although being able to predict stress-strain curves is an importantapplication of FEM and a highly desirable property for any machinelearning model to learn, it does not easily lend itself to interpretation. Specifically, there is no simple quantitative way to define whether two-world units.stress-s train curves are “close” or “similar” with real Given that stress-strain curves are oftentimes intermediary representations of a composite property that are used to derive more meaningful descriptors such as modulus, strength, and toughness, we decided to evaluate the model in an analogous fashion. The CNN prediction in the PCA latent space representation is transformed back to a stress-strain curve using PCA, and used to derive the predicted modulus, strength, and toughness of the composite. The predicted material descriptors are then compared with the actual material descriptors. In this way, MSE and MAE now have clearly interpretable units and meanings. The average performance of the model with respect to the error between the actual and predicted material descriptor values derived from stress-strain curves are presented in Table. The MAE for material descriptors provides an easily interpretable metric of model performance and can easily be used in any design specification to provide confidence estimates of a model prediction. When comparing the mean absolute error (MAE) to the range of values taken on by the distribution of material descriptors, we can see that the MAE is relatively small compared to the range. The MAE compared to the range is <10% for all material descriptors. Relatively tight confidence intervals on the error indicate that this model architecture is stable, the model performance is not heavily dependent on initialization, and that our results are robust to differenttrain-test splits of the data.Future workFuture work includes combining empirical models with optimization algorithms, such as gradient-based methods, to identify composite designs that yield complementary mechanical properties. The ability of a trained empirical model to make high-throughput predictions over designs it has never seen before allows for large parameter space optimization that would be computationally infeasible for FEM. In addition, we plan to explore different visualizations of empirical models-box” of such models. Applying machine in an effort to “open up the blacklearning to finite-element methods is a rapidly growing field with the potential to discover novel next-generation materials tailored for a variety of applications. We also note that the proposed method can be readily applied to predict other physical properties represented in a similar vectorized format, such as electron/phonon density of states, and sound/light absorption spectrum.ConclusionIn conclusion, we applied PCA and CNN to rapidly and accurately predict the stress-strain curves of composites beyond the elastic limit. In doing so, several novel methodological approaches were developed, including using the derived material descriptors from the stress-strain curves as interpretable metrics for model performance and dimensionalityreduction techniques to stress-strain curves. This method has the potential to enable composite design with respect to mechanical response beyond the elastic limit, which was previously computationally infeasible, and can generalize easily to related problems outside of microstructural design for enhancing mechanical properties.中文基于卷积神经网络的复合材料微结构应力-应变曲线预测查尔斯，吉姆，瑞恩，格瑞斯摘要应力-应变曲线是材料机械性能的重要代表，从中可以定义重要的性能，例如弹性模量，强度和韧性。
Kagome Spin Liquid戈薇的自旋液体
Second Renormalization
Kagome
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n,n ~n
~n Z 1n P n n'n ~n' ~n' n
Step I: Divide lattice to disjoint blocks. Diagonalize H on each Block.
block excitations are the ''atoms'' (composite particles)
Truncate: M lowest states per block
• The triangular lattice flows to chiral symmetry breaking, probably the 3 sublattice Neel phase.
• Future: Investigations of the quantum phase transition in the effective Hamiltonian by following the RG flow.
Effective Bond Interactions
h( corr) 12
0.953
S 1S 2l1b ˆl2c ˆ
0.2111 S1S2l1l2
0.053 S1 S2 ly1ly2
0.1079 S1 S2
整体立铣刀圆弧刃前刀面的磨削轨迹算法
机械设计与制造Machinery Design & Manufacture147第6期2021年6月整体立铳刀圆弧刃前刀面的磨削轨迹算法张潇然，罗斌，陈思远，程雪峰（西南交通大学机械工程学院，四川成都610031）摘要:针对圆弧立铳刀磨削中周齿前刀面与端齿前刀面的过渡问题，提出磨削圆弧刃前刀面的砂轮轨迹算法，以此实现 周齿与端齿前刀面的光滑连接。
定义了一种切深磨削点轨迹曲线，可以同时约束圆弧前刀面的宽度和前角；定义了圆弧刃在平面中的瞬时前刀面，计算在瞬时前刀面中的砂轮磨削轨迹和姿态,再经过空间坐标变换，得出砂轮实际加工轨迹。
通过C++将算法编写为相应程序，进行仿真和实际加工验证，所得验证结果证明了该方法的正确性和可行性。
关键词:立铳刀;磨削加工;端齿圆弧刃；前刀面中图分类号:TH16;TH161 文献标识码:A 文章编号:1001-3997(2021)06-0147-03The Grinding Algorithm for the Rake Face of the Arc Edge of the Integral End MillZHANG Xiao-ran, LUO Bin, CHEN Si-yuan, CHENG Xue-feng(School of Mechanical Engineering , Southwest Jiaotong University, Sichuan Chengdu 610031, China)Abstract :A iming at the transition problem between the rake f ace of p eripheral f lank and the rake f ace of e nd tooth in the circulararc end mill, proposing a grinding algorithm f or the rake face of the arc edge that can achieve smooth connection between thetwo. Defines a depth-of-depth curve that can simultaneously constrain the width and rake angle of t he arc rake f ace. Defines theinstantaneous rake f ace of the arc edge and calculates the grinding path and attitude of t he grinding wheel in it. After the space coordinate transformation, the actual machining track of t he grinding wheel is obtained. Programming the algorithm into corre sponding p rogram by C++, and p erformming the simulation and p rocessing verification. The obtained results prove the correctnessand f easibility of t he algorithm.Key Words :End Mill ； Grinding ； Arc Edge ； Rake Face1引言圆弧头立铳刀是目前常见的高速切削刀具,具有制造成本低、材料切除率大等特点。
Quantum oscillations of spin current through a III-V semiconductor loop
a r X i v :c o n d -m a t /0112244v 1 [c o n d -m a t .m e s -h a l l ] 13 D e c 2001Quantum oscillations of spin current through a III-V semiconductor loopA.G.Mal’shukov and V.ShlyapinInstitute of Spectroscopy,Russian Academy of Science,142190Troitsk,Moscow oblast,RussiaK. A.ChaoSolid State Theory,Department of Physics,Lund University,S-22362Lund,Sweden We have investigated the transport of spin polarization through a classically chaotic semiconductor loop with a strong Rashba spin-orbit interaction.We found that if the escape time of a particle is long enough,the configuration averaged spin conductance oscillates strongly with the geometric spin phase.We predict a sizable rotation of spin polarization along its flowing path across the loop from the injector to the collector.We have also discovered a quantized universal spin relaxation in a 2D reservoir connected to such a semiconductor loop.PACS numbers:72.25.-b,73.63.Kv,03.65.VfIn the emerging field of spin electronics,the recent achievement of spin injection into paramagnetic semi-conductors [1]makes it an urgent task to control the spin current in semiconductor nanostructures.The spin current in a 2D channel of narrow gap III-V semicon-ductor can be manipulated by taking advantage of the strong spin-orbit splitting of the conduction electron en-ergy,because the mechanism of such splitting produces a spin precession which depends on the electron quasi-momentum.One example is the spin valve transistor [2],in which spin polarisation precesses in a 2D semiconduc-tor channel between a ferromagnet spin injector and a ferromagnetic spin collector.The measured resistance is determined by the angle of spin rotation along the prop-agating path.This angle can be varied by adjusting the spin-orbit interaction (SOI)strength in the semiconduc-tor with an external gate [3].In this Letter we will investigate an interesting phe-nomenon which can be observed in a 2D semiconductor loop as shown in Fig.1.It is well known [4]that due to the SOI,when an electron travels along a closed path,its wave function accumulates an additional phase ψ.If the SOI is a linear function of the electron quasimomentum,this phase depends only on the shape and the length of the path.In multiconnected conductors the effect of this phase on electron transport is similar to the Aharonov-Bohm (AB)effect.For example,in a disordered 2D ring,ψadds itself to the AB phase in the Aronov-Altshuller-Spivak oscillation of the DC electric conductance [5],as well as to the AB oscillation of the electric conductance mesoscopic fluctuations [6].In this Letter,instead of the oscillation of the elec-tric current,we will study the effect of the spin phase on the quantum oscillation of the spin current.How-ever,we will assume the motion of electrons as ballistic along their classical trajectories,rather than a diffusive transport inside the loop [4,6].One such trajectory is schematically illustrated by the zigzag-lined path in Fig.1,although it can be curved by a smooth random potential produced by the modulation doped impurities.FIG.1:A schematic plot of the loop sample.The zigzag line represents classical trajectory a ,and the arrowed curve is the smooth l -path.n (l )is a vector normal to the l -path.We assume that the motion of a particle inside the loop is classically chaotic,and so the quasiclassic approach of Ref.[7]can be applied.Nevertheless,to calculate the spin current through the loop we need to generalize this method by taking into account the spin degree of freedom and the SOI.With this approach,we will calculate the average spin current.This implies that its mesoscopic fluctuations will be averaged out.The corresponding ex-perimental performance is,for example,to average the results measured with several gate voltage sweeps.We will also ignore the weak localization correction,which is small because our system has a large number of trans-port channels through the loop.We will show that the so calculated spin conductance oscillates as a function of the SOI strength,and consequently can be controlled by varying the gate voltage.We would like to emphasize that these quantum oscillations appear in the classical spin conductance,which is a drastically different phe-nomenon from the AB effect.The AB effect is abcent in the average spin current when the weak localization effects are ignored.Following the Landauer approach,to study the spin dependent conductance we defineg αβγδ=e 22at Fermi energy E F propagating from the channel n and the spin state αin the injector to the channel m and the spin state βin the collector.t αβnm itself is the αβ–element of the matrix t mn which operates on spin states.The usual spin independent electric conductance is sim-ply g =(e 2/h ) n,m,α,β|t αβnm |2.If a spin orinented along the x -axis is injected from the injector,and its orienta-tion becomes along the y -axis when the spin is collected at the collector,let g xy represent this spin current pass-ing through the loop.The matrix elements can then be written asg ij =e 2ha,bt 0(a )t ∗0(b )S αβa S γδ∗b,(4)where t 0(s )is the spin independent transmission ampli-tude for a classical trajectory labelled by s .One such tra-jectory is schematically plotteded in Fig.1as the zigzagline.The explicit expression of t 0(s)aswell as the bound-ary conditions are given in Ref.7.The spin evolution operator S a along the a –trajectory is defined asS a =T exp−iha|t 0(a )|2D aij .(6)whereD a ij =T r σi S a σj S †a.(7)Similarly,the so averaged electrical conductance is sim-ply (2e/h ) a |t 0(a )|2,and is spin independent.The evolution matrix can be parametrized using its property that it is a SU(2)representation of 3D rota-tions.In fact,we can express S a as a time ordered prod-uct of infinitesimal rotations corresponding to small shifts d r along the trajectory a .Each infinitesimal rotation is along the axis d r ×z through an angle 2|d r ×z |/L so .These infinitesimal rotations are represented by opera-tors exp[(−i/L so )(d r ×z )σ],and they sum up to make S a for a finite rotation through the angle 2ψa around a unit vector N a .Hence,the evolution matrix in (5)can be represented asS a =e iψa N a σ.(8)We should notice that ψa and N a are uniquely deter-mined by the geometric shape and the length of the tra-jectory a .From now on we will consider a particular sample ge-ometry that the area occupied by the 2D electron gas in the loop is much less than L 2so ,and the linear dimension of the loop can be larger than L so ,where L so = /αm ∗.In other word,both the upper path and the lower path of the loop are narrow.In this case one can show that each trajectory a in (5),as indicated by the zigzag line in Fig.1,can be replaced by a smooth trajectory,which is shown in Fig.1as the arrowed curve.We will label this smooth curve as l -path.Let θa be the area enclosed by the classical trajectory a making one turn around the loop.Then,the area enclosed by the l -path is the average of θa over classical trajectories.Deviations of real paths from the l -path can be treated perturbatively,which will be reported elsewhere.After the trajectory a is replaced by the l -path,the evolution matrix (5)becomes a simple function of the number w of windings the trajectory a makes around the loop until a particle escapes into the collector.w is posi-tive if the winding is counterclockwise.The correspond-ing evolution operator for the smooth l -path,denoted as S (w ),can be expressed asS (w )=e iψ0N 0σe iwψN σ.(9)Here ψ0and N 0are the 3D rotation parameters for the l -path in the lower half of the loop,and ψand N are the 3D rotation parameters for the l -path around the complete ing Eq.(9)we obtain the general dependence of the trace in (7)on the winding number D ij (w )=M (1)ij e i 2wψ+M (−1)ije−i 2wψ+M (0)ij ,(10)where the matrix elements M (1)ij =M (−1)∗ijdepend onlyon the geometric shape of the l -path.3 Based on the above expressions,we can follow the ap-proach used in Ref.9to calculate the Aharonov-Bohmeffect on mesoscopic electric conductancefluctuations indoubly connected classically chaotic loop.Let T be thetime interval that a particle spends inside the loop,andT0be such a duration for the shortest trajectory.Then,according to Ref.9,we average the winding number withthe Gaussian distribution functionP(w|T)= 2παT exp −w22T0/τβ≪1.Afteraveraging(10)over w and T we arrive atD ijw,T =M(0)ij+2Re[M(1)ij]A(ψ)(12)A(ψ)=κ2/(κ2+4sin2ψ).The oscillation pattern of the spin current,caused by the A(ψ)term,gets sharper asκbecomes smaller,and even-tually transforms into a periodic array of narrow peaks at positionsψ=πn.Eq.(12)provides a general relation between the spin conductance and the spin phaseψ.Here we will con-sider a specific example that the loop is nearly circular of radius d,and is symmetrically attached to two leads. For this geometry,by taking proper derivative with re-spect to the length of the l-path,we obtain from(5)the differential equationdSL so(n(l)·σ)S,(13)where the vector n(l)is shown in Fig.1.For a cicular l-path,this equation is equivalent to the time-dependent Schr¨o dinger equation for a11+4γ2,and the nonzero components of the spin conductance asg xx =−g0(π2/ψ2)[4γ2+A(ψ)cosψ]g xz =− g zx =g0(2γπ2/ψ2)[1−A(ψ)cosψ]g yy =−g0A(ψ)cosψg zz =g0(π2/ψ2)[1+4γ2A(ψ)cosψ].(14) From these expressions it is obvious that the oscillations of g can be observed as long as d≥L so.From Ref.3we evaluate L so≃3000˚A in InGaAs/InAlAs quantum wells. Hence,the loop size must be larger than about1µm but less that the electron dephasing length,which can be very long at low temperatures.So far we have considered the spin transport between the injector and the collector through the loop.The mechanism of transport process involves spin diffusion driven by the difference of spin polarizations between the lead attached to the injector and the lead attached to the collector.Such a transport is represented by the spin conductance(1)which,is determined by the spin dependent transmittance of the loop.Besides this pro-cess the SOI in the loop gives rise to a spin dependent reflectance.A particle which enters the loop from the injector-connected lead with a given spin orientation can be reflected back into the same lead with an opposite spin direction.This provides an additional relaxation process of the spin polarization in this lead,and the oscillatory dependence of such a relaxation on the spin phaseψis expected.A very suitable system for studying this relax-ation mechanism is a reservoir connected to a loop via a point contact which has N transmitting channels.The reservoir needs not to be very big.At a certain time,a nonequlibrium spin polarizationΣ=(N↑–N↓)/2is created in the reservoir,where Nσis the number of particles with spin projectionσonto the quantization axis.Let R↑↓be the reflectance associated to the electron spinflip reflec-tion.Then,the time rate of change ofΣis given bydΣ2hR↑↓(µ↑−µ↓)−Σ4 For smallκthe function[1–A(ψ)]oscillates betweenzero forψ=nπand a value very close to1forψ=(n+12)πthe spin relaxation rateΓisdetermined mainly by the ratio N/V.Taking a typ-ical value V=4µm2,and the electron effective mass m∗/m=0.03as in InAs,we obtainΓ≃N·109sec−1.The ”quantum”of relaxation time,10−9sec,is comparable to the intrinsic relaxation timeτs.We would like to em-phasize that at thisfixed spin phaseψ=(n+1。
第11届水科学发展论坛将在大连举办
International Journal for Numerical in Fluids, 2011,67(9):1160-1174.[2]王兴勇，索丽生，程永光，等.用Lattice Boltzmann方法模拟方柱绕流[J].河海大学学报（自然科学版），2003, 31 ( 3 )：259-263. (WANG Xingyong，SUOLisheng，CHENG Yongguang，et al. Simulation of flowfields around a square cylinder with Lattice BoltzmannMethod [ J ]. Journal of Hohai University ( NaturalScience)，2003,31(3) ：259-263. (in Chinese))[3]张兰丁.桥墩群体绕流的复变函数理论解[J].水利水电科技进展，2005,25 (1 ):14-16. (ZHANG Landing.Theoretical solution of complex function about flow aroundbridge piers[J]. Advances in Science and Technology ofWater Resources，2005,25(1) ：14-16. (in Chinese))[4] CAO S Y，GEY J，TAMURA Y. Shear effects on flow pasta square cylinder at moderate Reynolds numbers [ J].Journal of Engineering Mechanics，2012，138 (1)： 116123.[5] LANKADASU A，VENGADESAN S. Onset of vortexshedding in planar shear flow past a square cylinder[J].International Journal of Heat and Fluid Flow，2008,29(4) ：1054-1059.[ 6 ] HWANG R R， SUE Y C. Numerical simulation of shear effect on vortex shedding behind a square cylinder [J].International Journal for Numerical Methods in Fluids，1998,25(12) ：1409-1420.[7] AYUKAWA K，OCHI J，HIRAO T. Effects of shear rate onthe flow around a square cylinder in a uniform shear flow[J ]. Journal of Wind Engineering and IndustrialAerodynamics，1993,50(93) ：97-106.[8]陈明杰，施卫平.用格子Boltzmann方法计算剪切流的方柱绕流问题[J].吉林大学学报（理学版），2007,45(I)： 11-14. ( CHENG Mingjie，SHI Weiping. Numericalsimulation of linear shear flow past a square cylinder withLattice Boltzmann method [ J] . Journal of Jilin University(Science Edition)，2007,45(1) ：11-14. (in Chinese)) [ 9 ] SAHA A K， BISWAS G， MURALIDHAR K. Influence of inlet shear on structure of wake behind square cylinder[J]. Journal of Engineering Mechanics，1999,125 ： 359363.[10] WANG D G，WANG H J，XIONG J H，et al.Characteristic-based operator-splitting finite elementmethod for Navier-Stokes equations [ J ] . Science ChinaTechnological Sciences，2011，54(8)：2157-2166. [11] BREUER M，BERNSDORF J，ZEISER T，et al. Accuratecomputations of the laminar flow past a square cylinderbased on two different methods：Lattice-Boltzmann andfinite-volume[J]. International Journal of Heat and FluidFlow，2000,21(2)：186-196.[12] BREUER M，RODI W. Large eddy simulation for complexturbulent flows of practical interest [J]. Flow Simulationswith High-Performance Computer II，1996,52：258-274. [13] DAVIS R W，MOORE E F. A numerical study of vortexshedding from rectangles[J]. Journal of Fluid Mechanics，1982，116：475-506.[14] TREIDLER E B. An experimental and numericalinvestigation of flow past ribs in a channel[ R]. Berkeley：University of California，1991.[15] LI G，HUMPHREY J A C. Numerical modelling ofconfined flow past a cylinder of square cross-section atvarious orientations [ J ] . International Journal forNumerical Methods in Fluids，1995,20(21) ：1215-1236.[16] ARNAL M P，GOERING D J，HUMPHREY J A C. Vortexshedding from a bluff body adjacent to a pane siding wall[ J ] . Transaction of American Society of MechanicalEngineering，1991，113(3) ：384-398.[17] OKAJIMA A. Strouhal numbers of rectangular cylinders[J]. Journal of Fluid Mechanics，1982，123 ：379-398. [18] CHENG M，TAN S H N，HUNG K C. Linear shear flowover a square cylinder at low Reynolds number [ J ] .Physics of Fluids，2005，17(7) ：078103-1-78103^. [19] KWON T S，SUNG H J，HYUN J M，et al. Experimentalinvestigation of uniform-shear flow past a circular cylinder[J]. Journal of Fluids Engineering，1992，114(3) ： 457 -460.(收稿日期：2015 - 11 -07编辑:熊水斌）•简讯•第11届水科学发展论坛将在大连举办随着自然条件的变化和人类活动的加剧，水科 学问题越来越复杂。
Spin-dependent hole quantum transport in Aharonov-Bohm ring structure possible schemes for
1
arXiv:cond-mat/0508171v2 [cond-mat.mes-hall] 15 Sep 2005
The aim of using not only charge but also spin degree of freedom of electrons and holes in semiconductor electronic devices leads to a new field: semiconductor spintronics.1 Spin filter is one of the basic devices in this field. Many schemes for spin filters, most in electron systems, have been proposed2 in order to inject spin-polarized current into semiconductors, by means of spin-selective barriers, stubs,3 weak periodic magnetic modulations4,5 and anti-resonance effects in a doublebend structure.6 In this paper, we study the AB effect5,7 in twodimensional mesoscopic hole system. The interferences between the four spin states, i.e., the spin-up and -down heavy hole (HH) states and the spin-up and -down light hole (LH) states are more complicated than the electron system. Possible schemes for spin filter are proposed based on the abundant interference characteristics: When the Fermi energy of the lead is lower than the LH band edge of the frame, one can use the AB frame as a spin filter of HH by controlling the AB flux. When a suitable strain is applied on the frame to make the band edges of the HH and the LH close to each other, then if one injects a spin unpolarized HH current into the frame, a spin polarized LH (or HH) current can be obtained by controlling the AB flux. We consider the AB flux φ introduced by a homogeneous magnetic field B through a two-dimensional (2D) AB frame structure as shown in Fig. 1, which is grown in a (001) GaAs quantum well with a small well width √ (a = 10 nm). The momentum states along the growth direction (z ) are therefore quantized and one only need to consider the lowest subband. In this system there is no spin correlation a† ( a† ) between ak − 3 ak − 1 k3 k1 2 2 2 2 the spin-up and -down HH’s (LH’s). The spin-up HH’s (LH’s) are only coupled with the spin-down LH’s (HH’s). This can be seen from the Luttinger Hamiltonian8 HL in the momentum space with the matrix elements arranged
导电氧化铋薄膜的逆自旋霍尔效应
㊀第40卷㊀第10期2021年10月中国材料进展MATERIALS CHINAVol.40㊀No.10Oct.2021收稿日期:2021-01-25㊀㊀修回日期:2021-02-10基金项目:国家自然科学基金面上项目(11874098);兴辽英才计划资助项目(XLYC1807156);中央高校基本科研业务费专项资金资助项目(DUT20LAB111)第一作者:王孟怡,女,1995年生,硕士研究生通讯作者:邱志勇,男,1978年生,教授,博士生导师,Email:qiuzy@DOI :10.7502/j.issn.1674-3962.202101019导电氧化铋薄膜的逆自旋霍尔效应王孟怡,邱志勇(大连理工大学材料科学与工程学院三束材料改性教育部重点实验室辽宁省能源材料及器件重点实验室,辽宁大连116000)摘㊀要:自旋霍尔效应及其逆效应作为自旋电子学中实现自旋-电荷转换的核心物理效应,对纯自旋流的产生㊁探测有着重要的应用价值,是自旋电子器件开发与应用的关键技术节点㊂对高自旋-电荷转换效率材料体系的探索与开发是该领域的核心课题㊂以导电氧化铋薄膜为对象,研究其中的逆自旋霍尔效应㊂采用交流磁控溅射系统,使用氧化铋陶瓷靶制备了不同厚度的导电氧化铋薄膜,并与坡莫合金薄膜构成铁磁/非磁双层自旋泵浦器件,在该器件中首次观测并确认了导电氧化铋薄膜中逆自旋霍尔效应所对应的电压信号㊂通过逆自旋霍尔电压对氧化铋薄膜厚度的依存关系,定量地估算了氧化铋薄膜的自旋霍尔角及自旋扩散长度㊂通过提出一种新的具备可观测逆自旋霍尔效应的材料体系,不仅拓展了自旋电子材料的选择空间,也为新型自旋电子器件的设计和应用提供了思路㊂关键词:氧化铋;导电氧化物;逆自旋霍尔效应;自旋霍尔角;自旋扩散长度;自旋泵浦中图分类号:O469㊀㊀文献标识码:A㊀㊀文章编号:1674-3962(2021)10-0756-05Inverse Spin Hall Effect of Conductive Bismuth OxideWANG Mengyi,QIU Zhiyong(Key Laboratory of Energy Materials and Devices (Liaoning Province),Key Laboratory of Materials Modificationby Laser,Ion and Electron Beams,Ministry of Education,School of Materials Science and Engineering,Dalian University of Technology,Dalian 116000,China)Abstract :The direct and inverse spin Hall effect is the key effect for spin-charge conversion in spintronics,which plays avital role in the generation and detection of pure spin currents.It is a core issue to develop and explore materials with high spin-charge conversion efficiency.Here,we demonstrate the inverse spin Hall effect in a conductive bismuth oxide.The bis-muth oxide thin films with different thicknesses were prepared from a sintered bismuth oxide target by an rf-sputtering sys-tem.Then,permalloy /bismuth oxide bilayer spin pumping devices were developed,with which voltage signals corresponding to the inverse spin Hall effect were confirmed by the spin pumping technique.Furthermore,by systematical studying of bis-muth-oxide thickness dependence of those spin Hall voltages,the spin Hall angle and spin diffusion length were quantitative-ly estimated.Our results propose a novel system with an observable inverse spin Hall effect,which expands the possibility of spintronic materials and guides a new path for the development of spin-based devices.Key words :bismuth oxide;conductive oxide;inverse spin Hall effect;spin Hall angle;spin diffusion length;spin pumping1㊀前㊀言自旋电子学是以电子的量子自由度自旋为研究核心的新兴科研领域[1]㊂因在电子信息领域中的巨大应用潜力,自旋电子学建立伊始即吸引了众多研究者,现今是凝聚态物理领域不可忽视的科研分支之一㊂凝聚态体系中自旋的产生㊁操纵与检测相关的机理探讨和应用拓展是自旋电子学领域的核心课题[2]㊂本文所讨论的逆自旋霍尔效应即自旋霍尔效应的逆效应,是实现自旋流向电流转换的重要物理效应,其对自旋流特别是纯自旋流的检测有着不可替代的应用价值㊂逆自旋霍尔效应一方面可直接应用于弱自旋流的检测,另一方面也可作为自旋流-电流的转换媒介实现自旋向电荷体系的能量及信息传博看网 . All Rights Reserved.㊀第10期王孟怡等:导电氧化铋薄膜的逆自旋霍尔效应递[3-5]㊂而逆自旋霍尔效应的应用长期受制于自旋流-电流转换效率,即自旋霍尔角[6]㊂因此,新材料体系的探索及高自旋霍尔角材料的开发是逆自旋霍尔效应应用的关键所在㊂由于具有较大的自旋轨道耦合强度,重金属及其合金体系长期以来是高自旋霍尔角材料的研发重点[7-17]㊂其中贵金属Pt和Au的自旋霍尔角在室温附近分别可达11%ʃ8%和11.3%[7,8],是最常用的自旋霍尔材料㊂重金属合金AuW及CuBi报道的自旋霍尔角也达到10%以上[9,10]㊂此外,其它材料如半导体体系也是逆自旋霍尔效应的研究热点㊂2012年,Ando等[18]首次在室温下观测到p型半导体Si中的逆自旋霍尔效应,开拓了半导体中自旋霍尔效应及其逆效应的研究㊂此外,Olejník等[19]在外延的GaAs超薄膜中观测到逆自旋霍尔效应,并估算其自旋霍尔角θSHEʈ0.15%㊂有机聚合物体系中也被发现具有可观测的逆自旋霍尔效应[20,21]㊂Qaid等[20]在导电聚合物PEDOTʒPSS中观测到约2%的自旋霍尔角,进一步拓展了逆自旋霍尔效应的材料空间㊂另一方面,氧化物因其数量庞大的物质群及丰富多变的物理特性,一直以来都是凝聚态物理和材料研究的重点㊂而氧化物具有合成容易㊁性能稳定㊁价格低廉等特点,成为应用型功能材料的优先选项㊂自旋电子学领域的研究者很早就关注并对氧化物中的逆自旋霍尔效应进行了探索㊂在导电氧化物ITO㊁IrO2等材料中先后观测到逆自旋霍尔效应[22-24]㊂其中5d金属氧化物IrO2的自旋霍尔角达到6.5%[24],揭示了重金属氧化物作为自旋功能材料应用的可能,也拓展了氧化物体系中自旋霍尔功能材料的开发方向㊂本工作以导电氧化铋(Bi2O3)薄膜为研究对象,构建并制备了坡莫合金(Py)/Bi2O3的双层自旋泵浦器件㊂并利用自旋泵浦技术对Bi2O3中的逆自旋霍尔效应进行了系统的研究㊂首先在Bi2O3薄膜中观测并确认了逆自旋霍尔效应对应的电压信号;通过对Bi2O3薄膜厚度与信号强度的系统分析,确认该信号与自旋泵浦效应的等效电路模型预测相符;并定量地给出了Bi2O3薄膜的自旋霍尔角和自旋扩散长度㊂2㊀实验原理与方法本工作通过交流磁控溅射由烧结Bi2O3靶材制备了Bi2O3薄膜㊂通过控制成膜时气压(Ar:0.7Pa)及后期真空热处理工艺(<3ˑ10-5Pa,1h@500ħ),在具有热氧化层的硅基板上成功制备了导电Bi2O3薄膜㊂利用四端法确定Bi2O3薄膜的的电导率为2.1ˑ104Ω-1㊃m-1㊂通过改变成膜时间,系统地制备了膜厚范围在12~112nm的Bi2O3薄膜㊂并利用电子束沉积技术将10nm的Py薄膜与Bi2O3膜复合,构建了如图1a所示的Py/Bi2O3双层自旋泵浦器件㊂其中由10nm的Py单层薄膜测得的电导率为1.5ˑ106Ω-1㊃m-1㊂图1b是具有SiO2氧化层的硅基板上沉积的Py/Bi2O3双层膜的X射线衍射图谱,其中Py层与Bi2O3层的厚度分别为10和32nm㊂在2θ=69.1ʎ附近可观测到属于硅基板(400)晶面的强衍射峰;而2θ=27.7ʎ附近可以观测到微弱的特征衍射峰,对比衍射数据库可以判断该衍射峰来源于δ-Bi2O3的(111)晶面;除此之外,无明显可观测的衍射峰,由此判断器件中的Bi2O3为萤石结构的δ-Bi2O3相[25-27],并具备法线方向为[111]的择优取向㊂考虑到测得的薄膜电导率与离子导电的纯δ-Bi2O3的电导率之间存在差异[28],不能排除器件中的Bi2O3薄膜存在氧缺陷或伴生金属铋相从而导致薄膜的电导率上升㊂在衍射图谱中没有明显的氧化硅及Py特征峰,可以归因于氧化硅和Py均为非晶态结构且Py层膜厚过薄㊂图1㊀Py/Bi2O3双层膜器件及自旋泵浦实验设置示意图,H为外加磁场(a);具有SiO2氧化层的硅基板上Py/Bi2O3双层膜的X射线衍射图谱(b)Fig.1㊀Schematic illustration of the Py/Bi2O3bilayer system and spin-pumping set-up,H is the external magnetic field(a);XRD patterns of the Py/Bi2O3bilayer film on an oxidizedsilicon substrate(b)图1a还给出了自旋泵浦实验设置的示意图㊂实验样品置于TE011微波谐振腔中心,微波谐振腔特征频率为9.444GHz,此时样品处微波的电场分量取最小,而磁场分量取最大㊂同时在样品膜面方向上施加外磁场H㊂在微波的交变磁场与外磁场的共同作用下,当微波频率f 与外磁场大小H满足共振条件:757博看网 . All Rights Reserved.中国材料进展第40卷2πf =μ0γH FMR (H FMR +4πM s )(1)Py 中的铁磁共振被激发,其中γ和4πM s 分别是Py 薄膜的有效旋磁比和饱和磁化强度[29]㊂由自旋泵浦模型可知,此时Py 与Bi 2O 3薄膜界面产生自旋积累,纯自旋流J s 将通过界面注入到Bi 2O 3层中[20-22,29-36]㊂由于Bi 2O 3中的逆自旋霍尔效应,该自旋流将被转换为电流,并以电场E ISHE 的形式被检测㊂这里E ISHE :E ISHE ɖJ s ˑσ(2)其中,σ为磁性层的自旋极化矢量,E ISHE ,J s 与σ互为正交矢量时E ISHE 取最大值㊂E ISHE 可以通过Bi 2O 3表面两端的电极测量㊂3㊀结果与讨论图2a 给出了Py /Bi 2O 3双层膜器件中测得的典型铁磁共振微分吸收谱d I (H )/d H ㊂其中I 为微波吸收强度,H 为外磁场强度㊂由共振微分吸收谱可知,在H FMR ʈ99mT时,d I (H )/d H=0,即该磁场强度处微波吸收强度I 达到最大值,为Py 的铁磁共振场㊂图中正负峰值的间距对应图2㊀Py /Bi 2O 3双层膜铁磁共振微分吸收谱d I (H )/d H 和外加磁场H 的依存关系,I 为微波吸收强度(a);Py /Bi 2O 3双层膜中测得的电压信号V 与磁场强度H 的关系图,其微波功率为200mW(图中空心圆为实测数据,红色虚线为Lorentz 及其微分函数的拟合结果,蓝绿虚线分别为拟合曲线中的对称和反对称分量)(b)Fig.2㊀External magnetic field H dependence of the FMR signal d I (H )/d H for the Py /Bi 2O 3bilayer film,I denotes the microwave ab-sorption intensity (a);external magnetic field H dependence of the voltage signal V for the Py /Bi 2O 3bilayer film excited by mi-crowave with a power of 200mW (open circles are the experimen-tal data,the dash curves are the fitting results)(b)铁磁共振线宽W ,对比单层10nm 的Py 薄膜,Py /Bi 2O 3双层膜的铁磁共振线宽W 明显增大,表明在双层膜器件中由于铁磁共振的激发,产生了基于自旋泵浦效应的自旋流[31]㊂该自旋流通过Py /Bi 2O 3界面被注入到Bi 2O 3层㊂如图2b 所示,当固定微波功率为200mW 时,Py /Bi 2O 3双层膜在垂直于外磁场方向上可以测得与铁磁共振相对应的电压信号,其电压峰值对应的磁场基本与铁磁共振场H FMR 相符㊂利用Lorentz 及其微分函数拟合,可以很好地再现电压V 与磁场H 的依存关系(图2b)㊂其中,Lorentz 微分函数的反对称分量通常归因于自旋整流及其他效应的贡献[29,32-34]㊂从拟合参数可知反对称分量在整个电压信号中的占比小于5%㊂而Lorentz 函数的对称分量V s 主要归因于自旋泵浦产生的自旋流所对应的电压,其峰位与铁磁共振场H FMR 完全对应㊂同时考虑到无法排除对称信号中自旋整流效应的贡献,将电压信号中对称分量V s 定义为[28]:V s =V ISHE +V sr ㊂其中V ISHE 为逆自旋霍尔效应对应的电压信号,V sr 对应自旋整流效应的电压信号㊂图3a 和3b 分别给出了在外磁场方向不同的情况下测得的铁磁共振微分吸收谱d I (H )/d H 与电压信号V 对外磁场强度H 与铁磁共振场H FMR 的差值的依存关系图,其中外磁场方向角θH 的定义如图3c 中的插图所示㊂在改变外磁场方向角θH 的情况下,微波微分吸收谱的形状与线宽基本没有发生改变(图3a)㊂而电压信号V 随θH 的变化产生了较大的差异(图3b),当外磁场平行于膜面,即θH =ʃ90ʎ时,电压峰值取最大值,符号相反;当外磁场垂直于膜面,即θH =0ʎ时,电压峰信号消失㊂由式(2)可知,在自旋泵浦实验中逆自旋霍尔效应的信号大小与磁性层中的自旋极化方向相关,即E ISHE ɖsin θM ㊂这里θM 对应铁磁薄膜磁化方向与薄膜法线方向的夹角,可以根据铁磁共振场数据及外磁场方向角θH 计算获得[22,31,35]㊂考虑到薄膜样品中退磁场的影响,当且仅当磁场方向与膜面平行或在法线方向(即θH =ʃ90ʎ,0ʎ)时,铁磁薄膜的磁化方向与外磁场方向相同,此时E ISHE 取正负最大值和零㊂在Py /Bi 2O 3双层膜器件中测得的电压信号很好地符合了该实验模型㊂对所有外磁场方向角θH 下测得的电压数据进行Lorentz 及其微分函数拟合,分离出的电压信号对称分量V s 与外磁场方向角θH 的关系如图3c 所示㊂铁磁层Py 磁化强度M //H eff =H +H M ,这里H 为外加磁场,H M 为Py 薄膜的退磁场㊂V s 的磁场方向角θH 依存可以很好地基于自旋泵浦的动力学模型拟合[22,31,35,36],从而验证了V s中逆自旋霍尔效应的贡献占主导地位㊂857博看网 . All Rights Reserved.㊀第10期王孟怡等:导电氧化铋薄膜的逆自旋霍尔效应图3㊀不同外磁场方向角θH 下Py /Bi 2O 3双层膜的铁磁共振微分吸收谱d I (H )/d H (a)和电压信号V (b)与外磁场强度H 和铁磁共振场H FMR 差值的关系图;电压信号对称分量V s 与外磁场方向角θH 的关系图(实验数据表示为空心菱形,红色实线为拟合结果,插图中定义了外磁场方向角θH )(c)Fig.3㊀H -H FMR dependence of FMR signals d I (H )/d H (a)and voltagesignals V (b)for the Py /Bi 2O 3bilayer film at various out-planemagnetic field angles θH ;the out-plane magnetic field angle θHdependence of V s (the out-plane magnetic field angle θH is deter-mined in the insert)(c)㊀㊀图4a 中给出了在不同微波功率P MW 下的电压信号V 与外磁场H 的依存关系㊂与自旋泵浦模型的预期相符,电压峰值随着P MW 的增加而增大㊂图4b 为电压信号的对称分量V s 与微波功率P MW 的关系㊂由图可见,在微波功率为0~200mW 范围内,V s 与P MW 呈线性关系,与直流自旋泵浦模型的预测一致[22,30,35]㊂图5给出了Py /Bi 2O 3器件中的V s 对Bi 2O 3层厚度d N的依存关系㊂V s 随Bi 2O 3层厚度d N 的增大而减小,这基本可以归因于随Bi 2O 3层厚度d N 增加所导致的器件整体电阻的减小㊂该结果明显区别于Py /Bi 自旋泵浦器件中自旋泵浦信号随Bi层厚度的增加而先增加后减小的结图4㊀不同微波功率P MW 下的Py /Bi 2O 3双层膜的电压信号V 与磁场H 的关系图(a),电压信号对称分量V s 与微波功率P MW 的依存关系图(b)Fig.4㊀External magnetic field H dependence of voltage signals V for thePy /Bi 2O 3bilayer film at various microwave powers P MW (a),the P MW dependence of the voltage signal V s (b)果[37]㊂因此,在这里忽略可能存在的Rashba-Edelstein 效应等界面效应的影响,根据等效电路模型[29,31],同时考虑到Py 层中自旋整流效应的可能贡献,将V s 表示为[29]:V s =V ISHE +V sr=ωθSHE λtanh(d N /2λ)d N σN +d F σF 2e ћ()j 0s +j srd N σN +d F σF(3)其中,d N ㊁d F ㊁σN 和σF 分别表示Bi 2O 3层和Py 层的厚度d 和电导率σ;j 0s 是Py /Bi 2O 3界面处的自旋流密度,可以通过Py 层中铁磁共振线宽W 的变化量计算获得;j sr表示自旋整流效应对应的等效电流㊂利用式(3)对V s 与Bi 2O 3层厚度d N 依存关系的实验数据进行拟合,可以获得Bi 2O 3薄膜中的自旋霍尔角θSHE 及自旋扩散长度λ㊂如图5所示,拟合所得的θSHE 和λ的上限分别为0.7%和6.5nm,而θSHE 和λ的最佳估测值分别为0.5%和3.5nm㊂4㊀结㊀论本工作利用自旋泵浦效应首次在导电Bi 2O 3薄膜中观测并确认了逆自旋霍尔效应㊂在Py /Bi 2O 3双层膜中探测到的电压信号与逆自旋霍尔效应和自旋泵浦效应的模型相符㊂通过系统探讨逆自旋霍尔电压与Bi 2O 3薄膜厚度的关系,定量地给出了导电Bi 2O 3薄膜中的逆自旋霍尔角约为0.5%,自旋扩散长度约为3.5nm㊂导电Bi 2O 3中逆自旋霍尔效应的发现,不仅拓宽了逆自旋霍尔效应957博看网 . All Rights Reserved.中国材料进展第40卷图5㊀Py/Bi2O3双层膜中Bi2O3厚度d N与电压信号对称分量V s的依存关系(实验数据表示为空心圆,实线为式(3)的拟合结果,插图为Py/Bi2O3双层膜系统中考虑了逆自旋霍尔效应和自旋整流效应的等效电路图)Fig.5㊀The experimental and fitting results of Bi2O3thickness d N dependence of V s for the Py/Bi2O3bilayer films(the insert is theequivalent circuit of the Py/Bi2O3bilayer system,in which inversespin Hall effect and spin-rectification effect are both considered)材料的选择范围,也为新型自旋电子器件的设计和应用提供了新的选择㊂参考文献㊀References[1]㊀FLATTE M E.IEEE Transactions on Electron Devices[J],2007,54(5):907-920.[2]㊀TAKAHASHI S,MAEKAWA S.Science Technology Advanced Materi-als[J],2008,9(1):014105.[3]㊀SCHLIEMANN J.International Journal of Modern Physics B[J],2006,20:1015-1036.[4]㊀JUNGWIRTHT,WUNDERLICH J,OLEJNIK K.Nature Materials[J],2012,11(5):382-390.[5]㊀NIIMI Y,OTANI Y.Reports on Progress in Physics[J],2015,78(12):124501.[6]㊀SINOVA J,VALENZUELA S,WUNDERLICH J,et al.Reviews ofModern Physics[J],2015,87(4):1213-1260.[7]㊀SEKI T,HASEGAWA Y,MITANI S,et al.Nature Materials[J],2008,7(2):125-129.[8]㊀ALTHAMMER M,MEYER S,NAKAYAMA H,et al.Physical Re-view B[J],2013,87(22):224401.[9]㊀LACZKOWSKI P,ROJAS-SÁNCHEZ J C,SAVERO-TORRES M,etal.Applied Physics Letters[J],2014,104(14):142403. 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All Rights Reserved.㊀第10期中国材料进展特约编辑王聪特约编辑雷娜特约编辑刘恩克特约撰稿人方梅特约撰稿人魏大海王㊀聪:北京航空航天大学集成电路科学与工程学院教授,博士生导师㊂1995年在中国科学院物理研究所获得博士学位,曾先后在德国㊁法国㊁美国短期工作㊂长期从事反钙钛矿磁性功能材料㊁反铁磁自旋电子学材料,太阳能光热转换涂层㊁辐射致冷薄膜以及太阳能集热器等的研究㊂在Adv Mater,Phys Rev系列等刊物上发表论文近240篇,SCI他引超过3500次,2020年被评为爱思唯尔(Elsevier)中国被高引学者;授权国家发明专利13项,2012年获得教育部高等学校科学研究优秀成果自然科学二等奖;2020年获得中国材料研究学会科学技术二等奖㊂现兼任中国物理学会理事㊁中国晶体学会理事㊁中国物理学会粉末衍射专业委员会副主任㊁中国材料学会环境材料委员会副主任㊁国家能源太阳能热发电技术研发中心技术委员会委员㊁国际衍射数据中心(ICDD)委员㊁中国物理学会相图委员会委员㊁IEEE PES储能技术委员会(中国)储能材料与器件分委会委员㊂Journal of Solar EnergyResearch Updates主编㊂‘北京航空航天大学学报“‘硅酸盐学报“‘中国材料进展“等杂志编委㊂承担国家 863 项目,国家基金委重点项目等20余项,培养博士㊁硕士研究生近50名㊂雷㊀娜:女,1981年生,北京航空航天大学集成电路科学与工程学院副教授,博士生导师㊂主要研究方向为低维磁性材料的自旋调控,围绕电控磁的低功耗自旋存储与自旋逻辑器件方面取得一定成果,发表相关SCI论文30余篇,包括Nat Commun3篇,Phys Rev Lett,Phys RevAppl,Nanoscale各1篇等㊂其中1篇Nat Com-mun文章为ESI高被引论文;Phys Rev Appl上文章被编辑选为推荐文章㊂刘恩克:男,1980年生,中国科学院物理研究所研究员,博士生导师㊂2012年于中国科学院物理研究所获得博士学位,获中科院院长奖学金特别奖㊁中科院百篇优秀博士论文奖㊂2016~2018年作为 洪堡学者 赴德国马普所进行研究访问,合作导师为Claudia Felser和StuartParkin教授㊂主要从事磁性相变材料㊁磁性拓扑材料㊁磁性拓扑电/热输运等研究㊂在国际上首次实现了磁性外尔费米子拓扑物态,提出了全过渡族Heusler合金新家族,发现了 居里温度窗口 效应,提出了等结构合金化 方法等㊂已在Science,NatPhys,Nat Commun,SciAdv,PRL等期刊上发表学术论文200篇㊂曾获国家基金委 优青 基金㊁中科院青促会优秀会员基金㊁国家自然科学二等奖(4/5)等㊂方㊀梅:女,1984年生,中南大学物理与电子学院副教授,硕士生导师㊂长期从事功能薄膜㊁自旋电子器件的设计㊁制备与表征的研究工作,探索自旋电子学相关机理㊂以第一作者/通讯作者在Nature Com-munications(2篇)㊁Physical Review Applied,APL Materials,AppliedPhysics Letters等国际期刊上发表学术论文20余篇,获得国家授权发明专利1项㊂主持国家自然科学基金青年项目㊁湖南省自然基金面上项目㊁中国博士后科学基金一等资助和特别资助㊁中南大学 猎英计划 等项目多项㊂兼任PhysicalReview Letters,PhysicalReview Applied等10余个国际期刊审稿人㊂魏大海:男,1982年生,2009年博士毕业于复旦大学物理系,现任中国科学院半导体研究所研究员,博士生导师㊂2010~2015年先后在日本东京大学物性研究所㊁德国雷根斯堡大学开展博士后研究㊂主要致力于半导体自旋电子学的物理与器件研究,基于新型自旋电子材料开展注入㊁探测以及调控,通过自旋霍尔效应㊁自旋轨道矩等自旋相关输运现象,探索自旋流的各种新奇特性及其可能的应用㊂在Nature Com-munications㊁Phys RevLett,等期刊上发表40余篇论文㊂曾获 国家海外高层次青年人才 ㊁德国洪堡 学者奖金㊁亚洲磁学联盟青年学者奖,作为负责人入选首批中特约撰稿人邱志勇科院稳定支持基础研究领域青年团队 ,承担十三五 国家重点研发计划 量子调控与量子信息 专项青年项目㊂邱志勇:男,1978年生,大连理工大学材料科学与工程学院教授,博士生导师㊂长期从事功能材料与自旋电子学融合领域的研究工作,近年来在Nature Materi-als,Nature Comm,PRL,ACTA Mater等知名杂志上发表论文60余篇,H因子25,引用2200余次㊂依托材料开发背景,在自旋电子材料及自旋物理方向进行了长期研究,近两年以推进新一代磁存储器技术为目标,致力于反铁磁自旋电子学领域的开拓,取得了基于反铁磁材料的自旋物理及应用相关的一系列先驱性成果㊂167博看网 . 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Influenceofspin__省略_ionalelectrongas_颜玉珍
Flow equation renormalization of a spin-boson model with a structured bath
a r X i v :c o n d -m a t /0302357v 1 [c o n d -m a t .m e s -h a l l ] 18 F eb 2003Flow equation renormalization of a spin-boson model with astructured bathSilvia Kleffa ,1,Stefan Kehrein b ,Jan von Delft aa Lehrstuhl f¨u r Theoretische Festk¨o rperphysik,Ludwig-Maximilians Universit¨a t,Theresienstr.37,80333M¨u nchen,Germany bTheoretische Physik III –Elektronische Korrelationen und Magnetismus,Universit¨a t Augsburg,86135Augsburg,Germany1.Introduction -ModelRecently a new strategy for performing measure-ments on solid state (Josephson)qubits was proposed which uses the entanglement of the qubit with states of a damped oscillator [1],with this oscillator repre-senting the plasma resonance of the Josephson junc-tion.This system of a spin coupled to a damped har-monic oscillator (see Fig.1)can be mapped to a stan-dard model for dissipative quantum systems,namely the spin-boson model [2].Here the spectral function governing the dynamics of the spin has a resonance peak.Such structured baths were also discussed in con-nection with electron transfer processes [2].We use the flow equation method introduced by Wegner [3]to an-alyze the system shown in Fig.1,consisting of a two-2σx +ΩB †B +g (B †+B )σz +k˜ωk ˜b †k ˜b k+(B †+B )kκk (˜b †k +˜b k )+(B †+B )2 kκ2k2σx +1(Ω2−ω2)2+(2πΓωΩ)2with α=8Γg 2infinitesimal unitary transformations.The continuous sequence of unitary transformations U (l )is labelled by a flow parameter l .Applying such a transformation to a given Hamiltonian,this Hamiltonian becomes a function of l :H (l )=U (l )H U †(l ).Here H (l =0)=H is the initial Hamiltonian and H (l =∞)is the final diagonal ually it is more convenient to work with a differential formulation d H (l )dlU −1(l ).(3)Using the flow equation approach one can decouple system and bath by diagonalizing H (l =0)[4]:H (l =∞)=−∆∞2∆−ωk2q ,kλk λq I (ωk ,ωq ,l )(b k +b †k )(b q −b †q ),(5)with I (ωk ,ωq ,l )=ωqωk +∆+ωq −∆∂l=−2(ω−∆)2J (ω,l )(6)+2∆J (ω,l )d ω′J (ω′,l )I (ω,ω′,l ),d ∆ω+∆.(7)The unitary flow diagonalizing the Hamiltonian gener-ates a flow for σz (l )which takes the structure σz (l )=h (l )σz +σxkχk (l )(b k +b †k ),(8)where h (l )and χk (l )obey the differential equations dhωk +∆,(9)dχkωk +∆+qχq λk λq ∆I (ωk ,ωq ,l ).(10)One can show that the function h (l )decays to zero asl →∞.Therefore the observable σz decays completely into bath operators [4].J (ω)/Ωω/∆0C (ω)∆0Fig.2.(a)Different effective spectral functions J (ω,l =0)and(b)the corresponding C (ω)for ΩΓ=0.06and α=0.15.The inset shows the term scheme of a two-level system coupled to a harmonic oscillator for the two limits ∆0≪Ωand ∆0≫Ω.We integrated the flow equations numerically in or-der to calculate the Fourier transform,C (ω),of the spin-spin correlation function C (t )≡1[3]F.Wegner,Ann.Phys.3,77(1994).[4]S.Kehrein and A.Mielke,Ann.Phys.6,90(1997).3。
流体动力学中的分层流现象
流体动力学中的分层流现象引言流体动力学是研究流体运动规律和性质的科学，而分层流则是其中的一个重要现象。
分层流是指在一定条件下，流体在管道或容器中的流动呈现出分层分布的状态。
这种现象在地球科学、工程学以及生物学等领域中均有广泛应用。
本文将介绍流体动力学中的分层流现象以及相关的理论模型和实验方法。
分层流的定义与特征分层流是指流体在管道或容器中的流动呈现出分层分布的状态。
这种分层分布是由于流体中含有不同密度的组分，在受到外力作用时，根据密度大小而呈现出层次分明的结构。
分层流的特征包括：1.层次分明：不同密度的流体层在流动中明显区分，形成稳定的层级结构。
2.边界锐利：相邻不同密度流体层之间的边界清晰，通常是由于密度差异引起的。
分层流的形成与流体的密度及流速等参数有关，同时也受到外界条件的影响。
在一些实际系统中，分层流的形成可能涉及多种复杂的物理和化学过程。
分层流的理论模型为了描述和预测分层流现象，研究者们提出了一系列的理论模型。
其中最基本的理论模型是基于流体的密度分布函数，例如连续介质模型和多组分模型。
连续介质模型假设流体连续分布，并使用连续介质力学的方程描述流体运动。
多组分模型则考虑了流体中存在的多个组分，并根据各组分的密度和浓度等参数来描述分层流的形成。
除了基于密度分布函数的理论模型外，一些研究者还提出了基于流体动力学方程的理论模型。
这些模型通常采用Navier-Stokes方程描述流体的运动，并引入额外的方程来描述密度和浓度的变化。
这些模型更加适用于复杂的分层流问题，并能够考虑外界条件的影响。
分层流的实验方法为了研究分层流现象，研究者们开展了一系列的实验研究。
常用的实验方法包括：1.管道流动实验：通过在管道中注入具有不同密度的流体来观察分层流的形成和演化过程。
这种方法适用于需要研究管道中的流体分布情况的问题。
2.容器流动实验：在容器中注入不同密度的流体，并观察分层流的形成和演化过程。
这种方法适用于需要研究容器中流体分布情况的问题，例如海洋混合带的形成等。
中英文力学对准
一般力学类：分析力学 analytical mechanics拉格朗日乘子 Lagrange multiplier拉格朗日[量] Lagrangian拉格朗日括号 Lagrange bracket循环坐标 cyclic coordinate循环积分 cyclic integral哈密顿[量] Hamiltonian哈密顿函数 Hamiltonian function正则方程 canonical equation正则摄动 canonical perturbation正则变换 canonical transformation正则变量 canonical variable哈密顿原理 Hamilton principle作用量积分 action integral哈密顿-雅可比方程 Hamilton-Jacobi equation作用--角度变量 action-angle variables阿佩尔方程 Appell equation劳斯方程 Routh equation拉格朗日函数 Lagrangian function诺特定理 Noether theorem泊松括号 poisson bracket边界积分法 boundary integral method并矢 dyad运动稳定性 stability of motion轨道稳定性 orbital stability李雅普诺夫函数 Lyapunov function渐近稳定性 asymptotic stability结构稳定性 structural stability久期不稳定性 secular instability弗洛凯定理 Floquet theorem倾覆力矩 capsizing moment自由振动 free vibration固有振动 natural vibration暂态 transient state环境振动 ambient vibration反共振 anti-resonance衰减 attenuation库仑阻尼 Coulomb damping同相分量 in-phase component非同相分量 out-of -phase component超调量 overshoot 参量[激励]振动 parametric vibration模糊振动 fuzzy vibration临界转速 critical speed of rotation阻尼器 damper半峰宽度 half-peak width集总参量系统 lumped parameter system 相平面法 phase plane method相轨迹 phase trajectory等倾线法 isocline method跳跃现象 jump phenomenon负阻尼 negative damping达芬方程 Duffing equation希尔方程 Hill equationKBM方法 KBM method, Krylov-Bogoliu- bov-Mitropol'skii method马蒂厄方程 Mathieu equation平均法 averaging method组合音调 combination tone解谐 detuning耗散函数 dissipative function硬激励 hard excitation硬弹簧 hard spring, hardening spring谐波平衡法harmonic balance method久期项 secular term自激振动 self-excited vibration分界线 separatrix亚谐波 subharmonic软弹簧 soft spring ,softening spring软激励 soft excitation邓克利公式 Dunkerley formula瑞利定理 Rayleigh theorem分布参量系统 distributed parameter system优势频率 dominant frequency模态分析 modal analysis固有模态natural mode of vibration同步 synchronization超谐波 ultraharmonic范德波尔方程 van der pol equation频谱 frequency spectrum基频 fundamental frequencyWKB方法 WKB methodWKB方法Wentzel-Kramers-Brillouin method缓冲器 buffer风激振动 aeolian vibration嗡鸣 buzz倒谱cepstrum颤动 chatter蛇行 hunting阻抗匹配 impedance matching机械导纳 mechanical admittance机械效率 mechanical efficiency机械阻抗 mechanical impedance随机振动 stochastic vibration, random vibration隔振 vibration isolation减振 vibration reduction应力过冲 stress overshoot喘振surge摆振shimmy起伏运动 phugoid motion起伏振荡 phugoid oscillation驰振 galloping陀螺动力学 gyrodynamics陀螺摆 gyropendulum陀螺平台 gyroplatform陀螺力矩 gyroscoopic torque陀螺稳定器 gyrostabilizer陀螺体 gyrostat惯性导航 inertial guidance 姿态角 attitude angle方位角 azimuthal angle舒勒周期 Schuler period机器人动力学 robot dynamics多体系统 multibody system多刚体系统 multi-rigid-body system机动性 maneuverability凯恩方法Kane method转子[系统]动力学 rotor dynamics转子[一支承一基础]系统 rotor-support- foundation system静平衡 static balancing动平衡 dynamic balancing静不平衡 static unbalance动不平衡 dynamic unbalance现场平衡 field balancing不平衡 unbalance不平衡量 unbalance互耦力 cross force挠性转子 flexible rotor分频进动 fractional frequency precession半频进动half frequency precession油膜振荡 oil whip转子临界转速 rotor critical speed自动定心 self-alignment亚临界转速 subcritical speed涡动 whirl固体力学类：弹性力学 elasticity弹性理论 theory of elasticity均匀应力状态 homogeneous state of stress 应力不变量 stress invariant应变不变量 strain invariant应变椭球 strain ellipsoid均匀应变状态 homogeneous state of strain应变协调方程 equation of strain compatibility拉梅常量 Lame constants各向同性弹性 isotropic elasticity旋转圆盘 rotating circular disk 楔wedge开尔文问题 Kelvin problem布西内斯克问题 Boussinesq problem艾里应力函数 Airy stress function克罗索夫--穆斯赫利什维利法 Kolosoff- Muskhelishvili method基尔霍夫假设 Kirchhoff hypothesis板 Plate矩形板 Rectangular plate圆板 Circular plate环板 Annular plate波纹板 Corrugated plate加劲板 Stiffened plate,reinforcedPlate中厚板 Plate of moderate thickness弯[曲]应力函数 Stress function of bending 壳Shell扁壳 Shallow shell旋转壳 Revolutionary shell球壳 Spherical shell[圆]柱壳 Cylindrical shell锥壳Conical shell环壳 Toroidal shell封闭壳 Closed shell波纹壳 Corrugated shell扭[转]应力函数 Stress function of torsion 翘曲函数 Warping function半逆解法 semi-inverse method瑞利--里茨法 Rayleigh-Ritz method松弛法 Relaxation method莱维法 Levy method松弛 Relaxation量纲分析 Dimensional analysis自相似[性] self-similarity影响面 Influence surface接触应力 Contact stress赫兹理论 Hertz theory协调接触 Conforming contact滑动接触 Sliding contact滚动接触 Rolling contact压入 Indentation各向异性弹性 Anisotropic elasticity颗粒材料 Granular material散体力学 Mechanics of granular media热弹性 Thermoelasticity超弹性 Hyperelasticity粘弹性 Viscoelasticity对应原理 Correspondence principle褶皱Wrinkle塑性全量理论 Total theory of plasticity滑动 Sliding微滑Microslip粗糙度 Roughness非线性弹性 Nonlinear elasticity大挠度 Large deflection突弹跳变 snap-through有限变形 Finite deformation 格林应变 Green strain阿尔曼西应变 Almansi strain弹性动力学 Dynamic elasticity运动方程 Equation of motion准静态的Quasi-static气动弹性 Aeroelasticity水弹性 Hydroelasticity颤振Flutter弹性波Elastic wave简单波Simple wave柱面波 Cylindrical wave水平剪切波 Horizontal shear wave竖直剪切波Vertical shear wave体波 body wave无旋波 Irrotational wave畸变波 Distortion wave膨胀波 Dilatation wave瑞利波 Rayleigh wave等容波 Equivoluminal wave勒夫波Love wave界面波 Interfacial wave边缘效应 edge effect塑性力学 Plasticity可成形性 Formability金属成形 Metal forming耐撞性 Crashworthiness结构抗撞毁性 Structural crashworthiness 拉拔Drawing破坏机构 Collapse mechanism回弹 Springback挤压 Extrusion冲压 Stamping穿透Perforation层裂Spalling塑性理论 Theory of plasticity安定[性]理论 Shake-down theory运动安定定理 kinematic shake-down theorem静力安定定理 Static shake-down theorem 率相关理论 rate dependent theorem载荷因子load factor加载准则 Loading criterion加载函数 Loading function加载面 Loading surface塑性加载 Plastic loading塑性加载波 Plastic loading wave简单加载 Simple loading比例加载 Proportional loading卸载 Unloading卸载波 Unloading wave冲击载荷 Impulsive load阶跃载荷step load脉冲载荷 pulse load极限载荷 limit load中性变载 nentral loading拉抻失稳 instability in tension加速度波 acceleration wave本构方程 constitutive equation完全解 complete solution名义应力 nominal stress过应力 over-stress真应力 true stress等效应力 equivalent stress流动应力 flow stress应力间断 stress discontinuity应力空间 stress space主应力空间 principal stress space静水应力状态hydrostatic state of stress对数应变 logarithmic strain工程应变 engineering strain等效应变 equivalent strain应变局部化 strain localization应变率 strain rate应变率敏感性 strain rate sensitivity应变空间 strain space有限应变 finite strain塑性应变增量 plastic strain increment 累积塑性应变 accumulated plastic strain 永久变形 permanent deformation内变量 internal variable应变软化 strain-softening理想刚塑性材料 rigid-perfectly plastic Material刚塑性材料 rigid-plastic material理想塑性材料 perfectl plastic material 材料稳定性stability of material应变偏张量deviatoric tensor of strain应力偏张量deviatori tensor of stress 应变球张量spherical tensor of strain应力球张量spherical tensor of stress路径相关性 path-dependency线性强化 linear strain-hardening应变强化 strain-hardening随动强化 kinematic hardening各向同性强化 isotropic hardening强化模量 strain-hardening modulus幂强化 power hardening塑性极限弯矩 plastic limit bending Moment塑性极限扭矩 plastic limit torque弹塑性弯曲 elastic-plastic bending弹塑性交界面 elastic-plastic interface弹塑性扭转 elastic-plastic torsion粘塑性 Viscoplasticity非弹性 Inelasticity理想弹塑性材料 elastic-perfectly plastic Material极限分析 limit analysis极限设计 limit design极限面limit surface上限定理 upper bound theorem上屈服点upper yield point下限定理 lower bound theorem下屈服点 lower yield point界限定理 bound theorem初始屈服面initial yield surface后继屈服面 subsequent yield surface屈服面[的]外凸性 convexity of yield surface截面形状因子 shape factor of cross-section 沙堆比拟 sand heap analogy屈服Yield屈服条件 yield condition屈服准则 yield criterion屈服函数 yield function屈服面 yield surface塑性势 plastic potential能量吸收装置 energy absorbing device能量耗散率 energy absorbing device塑性动力学 dynamic plasticity塑性动力屈曲 dynamic plastic buckling塑性动力响应 dynamic plastic response塑性波 plastic wave运动容许场 kinematically admissible Field静力容许场 statically admissibleField流动法则 flow rule速度间断 velocity discontinuity滑移线 slip-lines滑移线场 slip-lines field移行塑性铰 travelling plastic hinge塑性增量理论 incremental theory ofPlasticity米泽斯屈服准则 Mises yield criterion普朗特--罗伊斯关系 prandtl- Reuss relation特雷斯卡屈服准则 Tresca yield criterion洛德应力参数 Lode stress parameter莱维--米泽斯关系 Levy-Mises relation亨基应力方程 Hencky stress equation赫艾--韦斯特加德应力空间Haigh-Westergaard stress space洛德应变参数 Lode strain parameter德鲁克公设 Drucker postulate盖林格速度方程Geiringer velocity Equation结构力学 structural mechanics结构分析 structural analysis结构动力学 structural dynamics拱 Arch三铰拱 three-hinged arch抛物线拱 parabolic arch圆拱 circular arch穹顶Dome空间结构 space structure空间桁架 space truss雪载[荷] snow load风载[荷] wind load土压力 earth pressure地震载荷 earthquake loading弹簧支座 spring support支座位移 support displacement支座沉降 support settlement超静定次数 degree of indeterminacy机动分析 kinematic analysis 结点法 method of joints截面法 method of sections结点力 joint forces共轭位移 conjugate displacement影响线 influence line三弯矩方程 three-moment equation单位虚力 unit virtual force刚度系数 stiffness coefficient柔度系数 flexibility coefficient力矩分配 moment distribution力矩分配法moment distribution method力矩再分配 moment redistribution分配系数 distribution factor矩阵位移法matri displacement method单元刚度矩阵 element stiffness matrix单元应变矩阵 element strain matrix总体坐标 global coordinates贝蒂定理 Betti theorem高斯--若尔当消去法 Gauss-Jordan elimination Method屈曲模态 buckling mode复合材料力学 mechanics of composites 复合材料composite material纤维复合材料 fibrous composite单向复合材料 unidirectional composite泡沫复合材料foamed composite颗粒复合材料 particulate composite层板Laminate夹层板 sandwich panel正交层板 cross-ply laminate斜交层板 angle-ply laminate层片Ply多胞固体 cellular solid膨胀 Expansion压实Debulk劣化 Degradation脱层 Delamination脱粘 Debond纤维应力 fiber stress层应力 ply stress层应变ply strain层间应力 interlaminar stress比强度 specific strength强度折减系数 strength reduction factor强度应力比 strength -stress ratio横向剪切模量 transverse shear modulus 横观各向同性 transverse isotropy正交各向异 Orthotropy剪滞分析 shear lag analysis短纤维 chopped fiber长纤维 continuous fiber纤维方向 fiber direction纤维断裂 fiber break纤维拔脱 fiber pull-out纤维增强 fiber reinforcement致密化 Densification最小重量设计 optimum weight design网格分析法 netting analysis混合律 rule of mixture失效准则 failure criterion蔡--吴失效准则 Tsai-W u failure criterion 达格代尔模型 Dugdale model断裂力学 fracture mechanics概率断裂力学 probabilistic fracture Mechanics格里菲思理论 Griffith theory线弹性断裂力学 linear elastic fracturemechanics, LEFM弹塑性断裂力学 elastic-plastic fracture mecha-nics, EPFM断裂 Fracture脆性断裂 brittle fracture解理断裂 cleavage fracture蠕变断裂 creep fracture延性断裂 ductile fracture晶间断裂 inter-granular fracture准解理断裂 quasi-cleavage fracture穿晶断裂 trans-granular fracture裂纹Crack裂缝Flaw缺陷Defect割缝Slit微裂纹Microcrack折裂Kink椭圆裂纹 elliptical crack深埋裂纹 embedded crack[钱]币状裂纹 penny-shape crack预制裂纹 Precrack 短裂纹 short crack表面裂纹 surface crack裂纹钝化 crack blunting裂纹分叉 crack branching裂纹闭合 crack closure裂纹前缘 crack front裂纹嘴 crack mouth裂纹张开角crack opening angle,COA裂纹张开位移 crack opening displacement, COD裂纹阻力 crack resistance裂纹面 crack surface裂纹尖端 crack tip裂尖张角 crack tip opening angle,CTOA裂尖张开位移 crack tip openingdisplacement, CTOD裂尖奇异场crack tip singularity Field裂纹扩展速率 crack growth rate稳定裂纹扩展 stable crack growth定常裂纹扩展 steady crack growth亚临界裂纹扩展 subcritical crack growth 裂纹[扩展]减速 crack retardation止裂crack arrest止裂韧度 arrest toughness断裂类型 fracture mode滑开型 sliding mode张开型 opening mode撕开型 tearing mode复合型 mixed mode撕裂 Tearing撕裂模量 tearing modulus断裂准则 fracture criterionJ积分 J-integralJ阻力曲线 J-resistance curve断裂韧度 fracture toughness应力强度因子 stress intensity factorHRR场 Hutchinson-Rice-Rosengren Field守恒积分 conservation integral有效应力张量 effective stress tensor应变能密度strain energy density能量释放率 energy release rate内聚区 cohesive zone塑性区 plastic zone张拉区 stretched zone热影响区heat affected zone, HAZ延脆转变温度 brittle-ductile transitiontemperature剪切带shear band剪切唇shear lip无损检测 non-destructive inspection双边缺口试件double edge notchedspecimen, DEN specimen单边缺口试件 single edge notchedspecimen, SEN specimen三点弯曲试件 three point bendingspecimen, TPB specimen中心裂纹拉伸试件 center cracked tension specimen, CCT specimen中心裂纹板试件 center cracked panelspecimen, CCP specimen紧凑拉伸试件 compact tension specimen, CT specimen大范围屈服large scale yielding小范围攻屈服 small scale yielding韦布尔分布 Weibull distribution帕里斯公式 paris formula空穴化 Cavitation应力腐蚀 stress corrosion概率风险判定 probabilistic riskassessment, PRA损伤力学 damage mechanics损伤Damage连续介质损伤力学 continuum damage mechanics细观损伤力学 microscopic damage mechanics累积损伤 accumulated damage脆性损伤 brittle damage延性损伤 ductile damage宏观损伤 macroscopic damage细观损伤 microscopic damage微观损伤 microscopic damage损伤准则 damage criterion损伤演化方程 damage evolution equation 损伤软化 damage softening损伤强化 damage strengthening 损伤张量 damage tensor损伤阈值 damage threshold损伤变量 damage variable损伤矢量 damage vector损伤区 damage zone疲劳Fatigue低周疲劳 low cycle fatigue应力疲劳 stress fatigue随机疲劳 random fatigue蠕变疲劳 creep fatigue腐蚀疲劳 corrosion fatigue疲劳损伤 fatigue damage疲劳失效 fatigue failure疲劳断裂 fatigue fracture疲劳裂纹 fatigue crack疲劳寿命 fatigue life疲劳破坏 fatigue rupture疲劳强度 fatigue strength疲劳辉纹 fatigue striations疲劳阈值 fatigue threshold交变载荷 alternating load交变应力 alternating stress应力幅值 stress amplitude应变疲劳 strain fatigue应力循环 stress cycle应力比 stress ratio安全寿命 safe life过载效应 overloading effect循环硬化 cyclic hardening循环软化 cyclic softening环境效应 environmental effect裂纹片crack gage裂纹扩展 crack growth, crack Propagation裂纹萌生 crack initiation循环比 cycle ratio实验应力分析 experimental stressAnalysis工作[应变]片 active[strain] gage基底材料 backing material应力计stress gage零[点]飘移zero shift, zero drift应变测量 strain measurement应变计strain gage应变指示器 strain indicator应变花 strain rosette应变灵敏度 strain sensitivity机械式应变仪 mechanical strain gage 直角应变花 rectangular rosette引伸仪 Extensometer应变遥测 telemetering of strain横向灵敏系数 transverse gage factor 横向灵敏度 transverse sensitivity焊接式应变计 weldable strain gage 平衡电桥 balanced bridge粘贴式应变计 bonded strain gage粘贴箔式应变计bonded foiled gage粘贴丝式应变计 bonded wire gage 桥路平衡 bridge balancing电容应变计 capacitance strain gage 补偿片 compensation technique补偿技术 compensation technique基准电桥 reference bridge电阻应变计 resistance strain gage温度自补偿应变计 self-temperature compensating gage半导体应变计 semiconductor strain Gage集流器slip ring应变放大镜 strain amplifier疲劳寿命计 fatigue life gage电感应变计 inductance [strain] gage 光[测]力学 Photomechanics光弹性 Photoelasticity光塑性 Photoplasticity杨氏条纹 Young fringe双折射效应 birefrigent effect等位移线 contour of equalDisplacement暗条纹 dark fringe条纹倍增 fringe multiplication干涉条纹 interference fringe等差线 Isochromatic等倾线 Isoclinic等和线 isopachic应力光学定律 stress- optic law主应力迹线 Isostatic亮条纹 light fringe 光程差optical path difference热光弹性 photo-thermo -elasticity光弹性贴片法 photoelastic coating Method光弹性夹片法 photoelastic sandwich Method动态光弹性 dynamic photo-elasticity空间滤波 spatial filtering空间频率 spatial frequency起偏镜 Polarizer反射式光弹性仪 reflection polariscope残余双折射效应 residual birefringent Effect应变条纹值 strain fringe value应变光学灵敏度 strain-optic sensitivity 应力冻结效应 stress freezing effect应力条纹值 stress fringe value应力光图 stress-optic pattern暂时双折射效应 temporary birefringent Effect脉冲全息法 pulsed holography透射式光弹性仪 transmission polariscope 实时全息干涉法 real-time holographicinterfero - metry网格法 grid method全息光弹性法 holo-photoelasticity全息图Hologram全息照相 Holograph全息干涉法 holographic interferometry 全息云纹法 holographic moire technique 全息术 Holography全场分析法 whole-field analysis散斑干涉法 speckle interferometry散斑Speckle错位散斑干涉法 speckle-shearinginterferometry, shearography散斑图Specklegram白光散斑法white-light speckle method云纹干涉法 moire interferometry[叠栅]云纹 moire fringe[叠栅]云纹法 moire method云纹图 moire pattern离面云纹法 off-plane moire method参考栅 reference grating试件栅 specimen grating分析栅 analyzer grating面内云纹法 in-plane moire method脆性涂层法 brittle-coating method条带法 strip coating method坐标变换 transformation ofCoordinates计算结构力学 computational structuralmecha-nics加权残量法weighted residual method有限差分法 finite difference method有限[单]元法 finite element method配点法 point collocation里茨法 Ritz method广义变分原理 generalized variational Principle最小二乘法 least square method胡[海昌]一鹫津原理 Hu-Washizu principle 赫林格-赖斯纳原理 Hellinger-Reissner Principle修正变分原理 modified variational Principle约束变分原理 constrained variational Principle混合法 mixed method杂交法 hybrid method边界解法boundary solution method有限条法 finite strip method半解析法 semi-analytical method协调元 conforming element非协调元 non-conforming element混合元 mixed element杂交元 hybrid element边界元 boundary element强迫边界条件 forced boundary condition 自然边界条件 natural boundary condition 离散化 Discretization离散系统 discrete system连续问题 continuous problem广义位移 generalized displacement广义载荷 generalized load广义应变 generalized strain广义应力 generalized stress界面变量 interface variable 节点 node, nodal point[单]元 Element角节点 corner node边节点 mid-side node内节点 internal node无节点变量 nodeless variable杆元 bar element桁架杆元 truss element梁元 beam element二维元 two-dimensional element一维元 one-dimensional element三维元 three-dimensional element轴对称元 axisymmetric element板元 plate element壳元 shell element厚板元 thick plate element三角形元 triangular element四边形元 quadrilateral element四面体元 tetrahedral element曲线元 curved element二次元 quadratic element线性元 linear element三次元 cubic element四次元 quartic element等参[数]元 isoparametric element超参数元 super-parametric element亚参数元 sub-parametric element节点数可变元 variable-number-node element拉格朗日元 Lagrange element拉格朗日族 Lagrange family巧凑边点元 serendipity element巧凑边点族 serendipity family无限元 infinite element单元分析 element analysis单元特性 element characteristics刚度矩阵 stiffness matrix几何矩阵 geometric matrix等效节点力 equivalent nodal force节点位移 nodal displacement节点载荷 nodal load位移矢量 displacement vector载荷矢量 load vector质量矩阵 mass matrix集总质量矩阵 lumped mass matrix相容质量矩阵 consistent mass matrix阻尼矩阵 damping matrix瑞利阻尼 Rayleigh damping刚度矩阵的组集 assembly of stiffnessMatrices载荷矢量的组集 consistent mass matrix质量矩阵的组集 assembly of mass matrices 单元的组集 assembly of elements局部坐标系 local coordinate system局部坐标 local coordinate面积坐标 area coordinates体积坐标 volume coordinates曲线坐标 curvilinear coordinates静凝聚 static condensation合同变换 contragradient transformation形状函数 shape function试探函数 trial function检验函数test function权函数 weight function样条函数 spline function代用函数 substitute function降阶积分 reduced integration零能模式 zero-energy modeP收敛 p-convergenceH收敛 h-convergence掺混插值 blended interpolation等参数映射 isoparametric mapping双线性插值 bilinear interpolation小块检验 patch test非协调模式 incompatible mode 节点号 node number单元号 element number带宽 band width带状矩阵 banded matrix变带状矩阵 profile matrix带宽最小化minimization of band width波前法 frontal method子空间迭代法 subspace iteration method 行列式搜索法determinant search method逐步法 step-by-step method纽马克法Newmark威尔逊法 Wilson拟牛顿法 quasi-Newton method牛顿-拉弗森法 Newton-Raphson method 增量法 incremental method初应变 initial strain初应力 initial stress切线刚度矩阵 tangent stiffness matrix割线刚度矩阵 secant stiffness matrix模态叠加法mode superposition method平衡迭代 equilibrium iteration子结构 Substructure子结构法 substructure technique超单元 super-element网格生成 mesh generation结构分析程序 structural analysis program 前处理 pre-processing后处理 post-processing网格细化 mesh refinement应力光顺 stress smoothing组合结构 composite structure流体动力学类：流体动力学 fluid dynamics连续介质力学 mechanics of continuous media介质medium流体质点 fluid particle无粘性流体 nonviscous fluid, inviscid fluid连续介质假设 continuous medium hypothesis流体运动学 fluid kinematics水静力学 hydrostatics 液体静力学 hydrostatics支配方程 governing equation伯努利方程 Bernoulli equation伯努利定理 Bernonlli theorem毕奥-萨伐尔定律 Biot-Savart law欧拉方程Euler equation亥姆霍兹定理 Helmholtz theorem开尔文定理 Kelvin theorem涡片 vortex sheet库塔-茹可夫斯基条件 Kutta-Zhoukowskicondition布拉休斯解 Blasius solution达朗贝尔佯廖 d'Alembert paradox 雷诺数 Reynolds number施特鲁哈尔数 Strouhal number随体导数 material derivative不可压缩流体 incompressible fluid 质量守恒 conservation of mass动量守恒 conservation of momentum 能量守恒 conservation of energy动量方程 momentum equation能量方程 energy equation控制体积 control volume液体静压 hydrostatic pressure涡量拟能 enstrophy压差 differential pressure流[动] flow流线stream line流面 stream surface流管stream tube迹线path, path line流场 flow field流态 flow regime流动参量 flow parameter流量 flow rate, flow discharge涡旋 vortex涡量 vorticity涡丝 vortex filament涡线 vortex line涡面 vortex surface涡层 vortex layer涡环 vortex ring涡对 vortex pair涡管 vortex tube涡街 vortex street卡门涡街 Karman vortex street马蹄涡 horseshoe vortex对流涡胞 convective cell卷筒涡胞 roll cell涡 eddy涡粘性 eddy viscosity环流 circulation环量 circulation速度环量 velocity circulation 偶极子 doublet, dipole驻点 stagnation point总压[力] total pressure总压头 total head静压头 static head总焓 total enthalpy能量输运 energy transport速度剖面 velocity profile库埃特流 Couette flow单相流 single phase flow单组份流 single-component flow均匀流 uniform flow非均匀流 nonuniform flow二维流 two-dimensional flow三维流 three-dimensional flow准定常流 quasi-steady flow非定常流unsteady flow, non-steady flow 暂态流transient flow周期流 periodic flow振荡流 oscillatory flow分层流 stratified flow无旋流 irrotational flow有旋流 rotational flow轴对称流 axisymmetric flow不可压缩性 incompressibility不可压缩流[动] incompressible flow 浮体 floating body定倾中心metacenter阻力 drag, resistance减阻 drag reduction表面力 surface force表面张力 surface tension毛细[管]作用 capillarity来流 incoming flow自由流 free stream自由流线 free stream line外流 external flow进口 entrance, inlet出口exit, outlet扰动 disturbance, perturbation分布 distribution传播 propagation色散 dispersion弥散 dispersion附加质量added mass ,associated mass收缩 contraction镜象法 image method无量纲参数 dimensionless parameter几何相似 geometric similarity运动相似 kinematic similarity动力相似[性] dynamic similarity平面流 plane flow势 potential势流 potential flow速度势 velocity potential复势 complex potential复速度 complex velocity流函数 stream function源source汇sink速度[水]头 velocity head拐角流 corner flow空泡流cavity flow超空泡 supercavity超空泡流 supercavity flow空气动力学 aerodynamics低速空气动力学 low-speed aerodynamics 高速空气动力学 high-speed aerodynamics 气动热力学 aerothermodynamics亚声速流[动] subsonic flow跨声速流[动] transonic flow超声速流[动] supersonic flow锥形流 conical flow楔流wedge flow叶栅流 cascade flow非平衡流[动] non-equilibrium flow细长体 slender body细长度 slenderness钝头体 bluff body钝体 blunt body翼型 airfoil翼弦 chord薄翼理论 thin-airfoil theory构型 configuration后缘 trailing edge迎角 angle of attack失速stall脱体激波detached shock wave 波阻wave drag诱导阻力 induced drag诱导速度 induced velocity临界雷诺数critical Reynolds number前缘涡 leading edge vortex附着涡 bound vortex约束涡 confined vortex气动中心 aerodynamic center气动力 aerodynamic force气动噪声 aerodynamic noise气动加热 aerodynamic heating离解 dissociation地面效应 ground effect气体动力学 gas dynamics稀疏波 rarefaction wave热状态方程thermal equation of state喷管Nozzle普朗特-迈耶流 Prandtl-Meyer flow瑞利流 Rayleigh flow可压缩流[动] compressible flow可压缩流体 compressible fluid绝热流 adiabatic flow非绝热流 diabatic flow未扰动流 undisturbed flow等熵流 isentropic flow匀熵流 homoentropic flow兰金-于戈尼奥条件 Rankine-Hugoniot condition状态方程 equation of state量热状态方程 caloric equation of state完全气体 perfect gas拉瓦尔喷管 Laval nozzle马赫角 Mach angle马赫锥 Mach cone马赫线Mach line马赫数Mach number马赫波Mach wave当地马赫数 local Mach number冲击波 shock wave激波 shock wave正激波normal shock wave斜激波oblique shock wave头波 bow wave附体激波 attached shock wave激波阵面 shock front激波层 shock layer压缩波 compression wave反射 reflection折射 refraction散射scattering衍射 diffraction绕射 diffraction出口压力 exit pressure超压[强] over pressure反压 back pressure爆炸 explosion爆轰 detonation缓燃 deflagration水动力学 hydrodynamics液体动力学 hydrodynamics泰勒不稳定性 Taylor instability 盖斯特纳波 Gerstner wave斯托克斯波 Stokes wave瑞利数 Rayleigh number自由面 free surface波速 wave speed, wave velocity 波高 wave height波列wave train波群 wave group波能wave energy表面波 surface wave表面张力波 capillary wave规则波 regular wave不规则波 irregular wave浅水波 shallow water wave深水波deep water wave重力波 gravity wave椭圆余弦波 cnoidal wave潮波tidal wave涌波surge wave破碎波 breaking wave船波ship wave非线性波 nonlinear wave孤立子 soliton水动[力]噪声 hydrodynamic noise 水击 water hammer空化 cavitation空化数 cavitation number 空蚀 cavitation damage超空化流 supercavitating flow水翼 hydrofoil水力学 hydraulics洪水波 flood wave涟漪ripple消能 energy dissipation海洋水动力学 marine hydrodynamics谢齐公式 Chezy formula欧拉数 Euler number弗劳德数 Froude number水力半径 hydraulic radius水力坡度 hvdraulic slope高度水头 elevating head水头损失 head loss水位 water level水跃 hydraulic jump含水层 aquifer排水 drainage排放量 discharge壅水曲线back water curve压[强水]头 pressure head过水断面 flow cross-section明槽流open channel flow孔流 orifice flow无压流 free surface flow有压流 pressure flow缓流 subcritical flow急流 supercritical flow渐变流gradually varied flow急变流 rapidly varied flow临界流 critical flow异重流density current, gravity flow堰流weir flow掺气流 aerated flow含沙流 sediment-laden stream降水曲线 dropdown curve沉积物 sediment, deposit沉[降堆]积 sedimentation, deposition沉降速度 settling velocity流动稳定性 flow stability不稳定性 instability奥尔-索末菲方程 Orr-Sommerfeld equation 涡量方程 vorticity equation泊肃叶流 Poiseuille flow奥辛流 Oseen flow剪切流 shear flow粘性流[动] viscous flow层流 laminar flow分离流 separated flow二次流 secondary flow近场流near field flow远场流 far field flow滞止流 stagnation flow尾流 wake [flow]回流 back flow反流 reverse flow射流 jet自由射流 free jet管流pipe flow, tube flow内流 internal flow拟序结构 coherent structure 猝发过程 bursting process表观粘度 apparent viscosity 运动粘性 kinematic viscosity 动力粘性 dynamic viscosity 泊 poise厘泊 centipoise厘沱 centistoke剪切层 shear layer次层 sublayer流动分离 flow separation层流分离 laminar separation 湍流分离 turbulent separation 分离点 separation point附着点 attachment point再附 reattachment再层流化 relaminarization起动涡starting vortex驻涡 standing vortex涡旋破碎 vortex breakdown 涡旋脱落 vortex shedding压[力]降 pressure drop压差阻力 pressure drag压力能 pressure energy型阻 profile drag滑移速度 slip velocity无滑移条件 non-slip condition 壁剪应力 skin friction, frictional drag壁剪切速度 friction velocity磨擦损失 friction loss磨擦因子 friction factor耗散 dissipation滞后lag相似性解 similar solution局域相似 local similarity气体润滑 gas lubrication液体动力润滑 hydrodynamic lubrication 浆体 slurry泰勒数 Taylor number纳维-斯托克斯方程 Navier-Stokes equation 牛顿流体 Newtonian fluid边界层理论boundary later theory边界层方程boundary layer equation边界层 boundary layer附面层 boundary layer层流边界层laminar boundary layer湍流边界层turbulent boundary layer温度边界层thermal boundary layer边界层转捩boundary layer transition边界层分离boundary layer separation边界层厚度boundary layer thickness位移厚度 displacement thickness动量厚度 momentum thickness能量厚度 energy thickness焓厚度 enthalpy thickness注入 injection吸出suction泰勒涡 Taylor vortex速度亏损律 velocity defect law形状因子 shape factor测速法 anemometry粘度测定法 visco[si] metry流动显示 flow visualization油烟显示 oil smoke visualization孔板流量计 orifice meter频率响应 frequency response油膜显示oil film visualization阴影法 shadow method纹影法 schlieren method烟丝法smoke wire method丝线法 tuft method。
基于密度泛函理论的KF-NaF-AlF3低温电解质体系势参数拟合及分子动力学模拟
第51卷第12期2020年12月中南大学学报(自然科学版)Journal of Central South University (Science and Technology)V ol.51No.12Dec.2020基于密度泛函理论的KF-NaF-AlF 3低温电解质体系势参数拟合及分子动力学模拟王景坤1,2，国辉1，张红亮1,3，李劼1,3(1.中南大学冶金与环境学院，湖南长沙，410083；2.中国宏桥集团有限公司，山东邹平，256200；3.中南大学难冶有色金属资源高效利用国家工程实验室，湖南长沙，410083)摘要：基于密度泛函理论构建KF-NaF-AlF 3熔盐体系的Buckingham 势参数，基于所构建的势参数对KF-NaF-AlF 3熔盐体系进行分子动力学模拟。
研究结果表明：熔盐中主要的阴离子构型为F −，［AlF 4］−，［AlF 5］2−和［AlF 6］3−；由于桥氟离子的存在，熔盐中形成了更复杂的Al-F-Al 络合离子构型，如［Al 2F 8］2−，［Al 3F 10］−，［Al 4F 14］2−，［Al 4F 15］3−和［Al 4F 16］4−等，这些复杂阴离子的存在可能会进一步降低KF-NaF-AlF 3熔盐的输运性能。
关键词：势参数拟合；KF-NaF-AlF 3；分子动力学模拟；离子结构中图分类号：TF821文献标志码：A开放科学(资源服务)标识码(OSID)文章编号：1672-7207（2020）12-3300-09Potential parameter fitting and molecular dynamics simulation of KF-NaF-AlF 3low temperature electrolyte system based on densityfunctional theoryWANG Jingkun 1,2,GUO Hui 1,ZHANG Hongliang 1,3,LI Jie 1,3(1.School of Metallurgy and Environment,Central South University,Changsha 410083,China;2.China Hongqiao Group Limited,Zouping 256200,China;3.National Engineering Laboratory for High Efficiency Recovery of Refractory Nonferrous Metals,Central South University,Changsha 410083,China)Abstract:Buckingham potential parameters of KF-NaF-AlF 3molten salt system were constructed based on density functional theory.Molecular dynamics simulation of KF-NaF-AlF 3molten salt system was carried out based on the constructed potential parameters.The results show that the main anion configurations in the molten salt are F −,[AlF 4]−,[AlF 5]2−and [AlF 6]3−.Due to the presence of bridge F ions,more complex Al-F-Al complex ion configurations are formed in the molten salt,such as [Al 2F 8]2−,[Al 3F 10]−,[Al 4F 14]2−,[Al 4F 15]3−and [Al 4F 16]4−,etc.TheDOI:10.11817/j.issn.1672-7207.2020.12.004收稿日期：2020−06−16；修回日期：2020−08−22基金项目(Foundation item)：国家自然科学基金面上项目(51974373，51674300，51874365，61751312)；湖南省自然科学基金面上项目(2018JJ2521)(Projects(51974373,51674300,51874365,61751312)supported by the National Natural Science Foundation of China;Project(2018JJ2521)supported by the Natural Science Foundation of Hunan Province)通信作者：李劼，博士，教授，从事铝电解基础理论及智能优化制造研究；E-mail ：138****************第12期王景坤，等：基于密度泛函理论的KF-NaF-AlF3低温电解质体系势参数拟合及分子动力学模拟existence of these complex anions may further reduce the transport performance of the molten salt KF-NaF-AlF3.Key words:potential parameter fitting;KF-NaF-AlF3;molecular dynamics simulation;ionic structure电解铝工艺是一种能耗较高的工艺，生产1tAl电解铝消耗电12000~14000kW·h(电力成本占电解铝总成本的35%~40%)。
guo_guang_yu
2. Spin Hall effect
1) The Hall Effect
Ordinal Hall Effect (1879)
Anomalous Hall Effect (Hall, 1880 & 1881) (Extraordinary or spontaneous Hall effect)
Zoo of the Hall Effects
Acknowledgements: Co-Authors:
Qian Niu (UTAustin), Yugui Yao (CAS,Beijing) Stimulating Discussions: Ming-Che Chang (NTNU, Taipei). Financial Support: National Science Council.
(k )
n ' n
FM bcc Fe
G. S. Krinchik and V. S. Gushchin, Sov. Phys.-JETP 24, 984 (1969).
P.N. Dheer,Phys.Rev 156, 637(1967) 1032 (ohm cm)-1
(4) Berry phase formalism for Hall effects
Schematic band pictures of (a) non-magnetic metals, (b) ferromagnetic metals and (c) halfmetallic metals .
Spin filter
[Slobodskyy, et al., PRL 2003]
Problems: magnets and/or magnetic fields needed, and difficult to integrate with semiconductor technologies.
铜管弯曲缺陷分析及退火工艺优化
铜管弯曲缺陷分析及退火工艺优化刘锦平;杨湘杰;罗欣;朱晖;余琪;乐顺聪【摘要】The inner wrinkle is a kind of frequent defects during the bending of thin-wall copper tube. The cau-sing reason of copper tube inner wrinkle defects was analyzed by finite element software and inner wrinkle sample microstructure. The microstructure was characterized at different annealing process and then the annealing process was optimized. These research results showed that the spiral motion of particle occurred at medial tube at the begin-ning of bending. The coarse grain obviously appeared at the wrinkle. The spiral motion of particle and the coarse grain would easily cause the wrinkle of tube,it meets with the actual bending results. The copper with fine and uni-form structure was obtained by annealing at500 ℃,33 min and was bended at site,and the excellent elbow tubes were obtained without the defect of inside wrinkle.%内皱是薄壁铜管弯曲过程中的一种常见缺陷.采用有限元软件并结合内皱样品微观组织分析了铜管产生内皱原因.对不同退火工艺条件下铜管的微观组织进行了表征,优化了铜管的退火工艺.研究结果表明:在弯曲变形的起始阶段,铜管内侧质点发生螺旋运动,铜管内皱处可见粗大晶粒,质点的螺旋运动和粗大晶粒易导致铜管弯曲时产生内皱,这与实际变形结果较为一致.在500℃、33 min退火时铜管微观组织细小均匀,对其进行现场弯曲试验,没有内皱缺陷,并获得了优良的小弯头管.【期刊名称】《南昌大学学报（工科版）》【年(卷),期】2017(039)004【总页数】6页(P366-371)【关键词】铜管;缺陷;退火;温度;晶粒【作者】刘锦平;杨湘杰;罗欣;朱晖;余琪;乐顺聪【作者单位】江西铜业集团公司,江西南昌330096;江西理工大学材料科学与工程学院,江西赣州341000;南昌大学机电工程学院,江西南昌330031;南昌大学机电工程学院,江西南昌330031;江西铜业集团公司,江西南昌330096;江西铜业集团公司,江西南昌330096;江西铜业集团公司,江西南昌330096;江西铜业集团公司,江西南昌330096【正文语种】中文【中图分类】TF124铜管广泛应用于空调制冷行业的“两器”(蒸发器、冷凝器)和连接管件[1-3]。
Berry phase
d p ε tr[ μ S F (p) ν S F (p) λ S F (p)]
3 μνλ
1
1
1
• Hall Conductance in terms of momentum space topology
Intrinsic spin Hall effect in p-type semiconductors
Motivations
• Electrons carry both charge and spin • Charge transport has been exploited in Electric and Electronic Engineering: Numerous applications in modern technology • Spin Transport of Electrons Theory: Spin-orbit coupling and spin transport Experiment: Induce and manipulate spin currents Spintronics and Quantum Information processing • Intrinsic Spin Hall Effect: Impurity-Independent Dissipation-less Current
up-spin down-spin
impurity
Cf. Mott scattering
•
The Intrinsic Spin Hall Effect Berry phase in momentum space Independent of impurities
Berry Phase (Vector Potential) in Momentum Space from Band Structure
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1
arXiv:cond-mat/0508116v2 [cond-mat.dis-nn] 26 Oct 2005
We present a numerical study of the spin Hall effect in a two-dimensional hole gas (2DHG) system in the presence of disorder. We find that the spin Hall conductance (SHC), extrapolated to the thermodynamic limit, remains finite in a wide range of disorder strengths for a closed system on torus. But there is no intrinsic spin Hall accumulation as induced by an external electric field once the disorder is turned on. The latter is examined by performing a Laughlin’s Gedanken gauge experiment numerically with the adiabatic insertion of a flux quantum in a belt-shaped sample, in which the absence of level crossing is found under the disorder effect. Without disorder, on the other hand, energy levels do cross each other, which results in an oscillating spin-density-modulation at the sample boundary after the insertion of one flux quantum in the belt-shaped system. But the corresponding net spin transfer is only about one order of magnitude smaller than what is expected from the bulk SHC. These apparently contradictory results can be attributed to the violation of the spin conservation law in such a system. We also briefly address the dissipative Fermi surface contribution to spin polarization, which may be relevant to experimental measurements.
I.
INTRODUCTION
Recently it has been proposed1,2 that in spin-orbit coupling (SOC) systems one may use an electric field to generate transverse spin currents in the absence of external magnetic fields. It has been argued1,2 that such a spin Hall effect (SHE) is intrinsic, contributed by all the electrons below the Fermi energy, and the corresponding spin currents are “dissipationless” as in contrast to the dissipative longitudinal charge currents which are only contributed by the electrons close to the Fermi energy and are strongly subjected to scattering effects. The original proposals for the SHE are for the disorderfree cases.1,2 In the two-dimensional (2D) electron gas described by the Rashba model,2 it was shown based on a perturbative approach3,4 that the SHC is precisely cancelled by the vertex correction once the disorder is turned on. On the other hand, the vertex correction is found to vanish5 for the three-dimensional (3D) p-doped semiconductors described by the Luttinger model1 so that the SHC is still finite in the presence of weak disorder. Numerical calculations6–8 of the SHC seem to support such perturbative results of the distinct behavior for two models in the thermodynamic limit. Experimentally the signatures of spin polarization have been observed recently in 2DHG system9 and 3D ndoped semiconductors,10 which have generated a lot of excitement concerning whether they are due to the intrinsic SHE mentioned above or some extrinsic effect.11 Bernevig and Zhang have shown that the vortex correction does vanish in the 2DHG12 and 3D n-doped semiconductor13 systems. Furthermore, the mesoscopic SHE in the 2DHG is also found to be present based on the nonequilibrium Green function method14 and LandauerB¨ uttiker formula with attached leads,15 similar to (with larger magnitude than) the mesoscopic SHE found in the 2D Rashba model.16,17 But it is still unclear whether the bulk SHE in the 2DHG can survive in the thermodynamic limit beyond the perturbative approach.
In this paper, we perform numerical calculations for the 2DHG in the presence of disorder. We first show that the bulk SHC calculated from the Kubo formula is indeed robust against the disorder in extrapolation to the thermodynamic limit, which is consistent with the vertex correction calculation.12 It is also similar to the behavior for the Luttinger model,7 but is in opposite to that of the 2D Rashba model.6 But when we perform a Laughlin’s Gedanken “gauge experiment” on a belt-shaped sample to probe the spin transfer/accumulation due to the SHE, we obtain a null result due to the anticrossing between energy levels, which is quite similar to what has been previously seen in the 2D Rashba model.6 We point out that the absence of edge states in the 2DHG system causes the general level repulsion with the turn on of disorder, which leads to the disappearance of the net spin Hall accumulation in an open system. Furthermore, at zero disorder case, energy levels do cross each other and we find an oscillating spin-density-modulation at the sample boundary after an adiabatic insertion of a flux quantum in the above-mentioned Laughlin’s gauge experiment. However, the corresponding net spin transfer is only about one order of magnitude smaller than what is expected from the calculated bulk SHC. We discuss the “conflicting” results of a finite SHC but without an intrinsic spin accumulation in the 2DHG, and point out that the underlying reason can be attributed to the violation of the spin conservation law in such a SOC system, where the SHC is no longer an unambiguous quantity for describing the spin transport. We also address the addition dissipative Fermi surfwhich may be relevant to experimental measurement.9,10 The remainder of the paper is organized as follows. In Sec. II, we numerically compute the SHC through the Kubo formula in a tight-binding model of the 2DHG system at different sample sizes and disorder strengths, and perform finite-size scaling analysis. In Secs. III A, III B and III C, we perform a Laughlin’s gauge experiment numerically to determine the intrinsic spin trans-