Internal Symmetry Group and Density Matrix of Fields with Spins 0, 1

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材料科学与工程专业英语词汇

材料科学与工程专业英语词汇1. 物理化学物理化学是研究物质结构、性质、变化规律及其机理的基础科学，是材料科学与工程的重要理论基础之一。

物理化学主要包括以下几个方面：热力学：研究物质状态和过程中能量转换和守恒的规律。

动力学：研究物质变化过程中速率和机理的规律。

电化学：研究电流和物质变化之间的相互作用和关系。

光化学：研究光和物质变化之间的相互作用和关系。

表面化学：研究物质表面或界面处发生的现象和规律。

结构化学：研究物质分子或晶体结构及其与性质之间的关系。

统计力学：用统计方法处理大量微观粒子行为，从而解释宏观物理现象。

中文英文物理化学physical chemistry热力学thermodynamics动力学kinetics电化学electrochemistry光化学photochemistry表面化学surface chemistry结构化学structural chemistry统计力学statistical mechanics状态方程equation of state熵entropy自由能free energy化学势chemical potential相平衡phase equilibrium化学平衡chemical equilibrium反应速率reaction rate反应级数reaction order反应机理reaction mechanism活化能activation energy催化剂catalyst电池battery电极electrode电解质electrolyte电位potential电流密度current density法拉第定律Faraday's law腐蚀corrosion中文英文光敏材料photosensitive material光致变色photochromism光致发光photoluminescence光催化photocatalysis表面张力surface tension润湿wetting吸附adsorption膜membrane分子轨道理论molecular orbital theory晶体结构crystal structure点阵lattice空间群space group对称元素symmetry element对称操作symmetry operationX射线衍射X-ray diffraction2. 量子与统计力学量子与统计力学是物理学的两个重要分支，是材料科学与工程的重要理论基础之一。

材料科学基础_概念中英文

材料科学基础重要概念（中英文）晶体学基础晶体学（crystallography）布喇菲点阵（Bravais lattice）晶体生成学（crystallogeny）体心化（body centering）晶体结构学（crytallogy）底心化（base centering）晶体化学（crystallochemistry）特殊心化（special centering）晶体结构（crystal structure）晶面（crystal plane）点阵平移矢量（lattice translation vector）晶（平）面指数（crystal – plane indice）初级单胞（primitive cell）晶带（zone）点阵常数（lattice parameter）倒易空间（reciprocal space）对称变换（symmetry translation）参考球（reference sphere）主动操作（active operation）经线（longitude）国际符号（international notation）赤道平面（equator plane）点对称操作（point symmetry operation）极网（pole net）旋转操作（rotation operation）结构基元（motif）二次旋转轴（two - fold axe, diad）晶体几何学（geometrical crystallography）四次旋转轴（four – fold axe, tetrad）晶体物理学（crystallographysics）镜像（mirror image）等同点（equivalent point）对形关系（enantiomorphic relation）点阵（lattice）反演（inversion）初基矢量（primitive translation vector）晶系（crystal system）复式初基单胞（multiple – primitive cell）单斜晶系（monoclinic system）对称元素（symmetry element）四方晶系（正方晶系）（tetragonal system）对称群（symmetry group）六方晶系（hexagonal system）被动操作（passive operation）熊夫利斯符号（Schoenflies notation）点阵有心化（centering of lattice）恒等操作（单位操作）（identity）面心化（face centering）旋转轴（rotation axe）单面心化（one – face centering）三次旋转轴（three – fold axe, triad）晶向（crystal direction）六次旋转轴（six – fold axe, hexad）晶向（方向）指数（crystal – direction indice）镜面（mirror plane）晶面族（form of crystal - plane）同宇（congruent）倒易点阵（reciprocal lattice）旋转反演（rotation - inversion）极射赤面投影（stereographic projection）三斜晶系（triclinic system）参考网络（reference grid）正交晶系（斜方晶系）（orthogonal system）纬线（latitude）立方晶系（cubic system）吴氏网（Wulff net）菱方晶系（rhombohedral system）标准投影网（standard projection）晶体结构晶体结构（crystal structure）鲍林规则（Pauling’s rule）结构符号（structure symbol）氧化物结构（oxide structure）致密度（空间填充效率）（efficiency of space 岩盐结构（rock structure）filling）纤维锌矿结构（wurtzite structure）配位数（coordination number）闪锌矿结构（zinc blende structure）配位多面体（coordination polyhedra）尖晶石结构（spinel structure）拓扑密堆相（topologically close – packed α-Al2O3型结构（corundum structure）phase）金红石结构（rutile structure）金属晶体（metal crystal）萤石结构（fluorite structure）离子晶体（ionic crystal）钙钛矿结构（perovskite structure）共价晶体（covalent crystal）钛铁矿结构（ilmenite structure）分子晶体（molecular crystal）氯化铯结构（cesium chloride structure）原子半径和离子半径（atomic radius and ionic 硅酸盐（silicate）radius）链状硅酸盐（chain silicate）原子结构体积（volume of structure per atom）层状硅酸盐（phyllo silicate）体密度（volumetric density,ρV）岛状硅酸盐（island silicate）面密度（planar density, ρP）骨架结构（framework structure）线密度（linear density, ρL）镁橄榄石结构（forsterite structure）金刚石结构（diamond structure）辉石（picrite）纳米碳管（carbon nano tube）粘土矿（clay mineral）置换固溶体（substitutional solid solution）高岭石（kaolinite）填隙固溶体（interstitial solid solution）云母（mica）尺寸因素（size factor）石英（quartz）价电子浓度（valance electron concentration）鳞石英（tridymite）电子化合物（electron compound）方石英（cristobalite）间隙化合物（interstitial compound）钙长石（anorthite）尺寸因素化合物（size–factor compound）分子筛（molecule sift）Laves相(Laves phase) 同素异构性（allotropy）σ相（σphase）多形性（polymorphism）有序固溶体（超结构）[ordered solid solution 准晶（quasicrystal）(super lattice) ] 彭罗斯拼砌（Penrose tiling）长程有序参数（long-range order parameter）短程有序参数（shot-range order parameter）晶体缺陷不完整性（imperfection）向错（disclination）点缺陷（point imperfection）沃特拉过程（V olterra’s process）空位（vacancy）刃型位错（edge dislocation）自间隙原子（self-interstitial）螺型位错（screw dislocation）构型熵（configuration entropy）混合型位错（mixed dislocation）肖脱基缺陷（Schottky defect）柏氏回路（Burgers circuit）弗兰克缺陷（Frenkel defect）柏氏矢量（Burgers vector）内禀点缺陷（intrinsic point defect）位错环（dislocation loop）非禀点缺陷（extrinsic point defect）位错密度（dislocation density）线缺陷（line imperfection）位错的弹性能（elastic energy of dislocation）位错（dislocation）位错线张力（tension of dislocation）位错宽度（width of dislocation）层错矢量（fault vector）保守运动（conservative motion）外延层错（extrinsic fault）非保守运动（nonconservative motion）层错能（stacking fault energy）滑移（slip）肖克莱部分为错（Shockley partial dislocation）滑动（glissile）铃木气团（Suzuki atmosphere）攀移（climb）弗兰克位错（Frank partial dislocation）自力（self-force）扩展位错（extended dislocation）渗透力（osmotic force）压杆位错（stair-rod partial dislocation）映像力（image force）Lomer-Cottrell 位错（Lomer-Cottrell弯结（kink）dislocation）割阶（jog）L-C阻塞（L-C Lock）柯垂尔气体（Cottrell atmosphere）赫斯阻塞（Hirth lock）史诺克气体（Snoek atmosphere）分位错（fractional dislocation）弗兰克-瑞德位错源（Frank-Read source）超点阵（superlattice）B-H位错源（Bardeen-Herring source）反相畴（Antiphase domain）位错塞积群（dislocation pile-up group）反相畴界（Antiphase boundary, APB）全位错（perfect dislocation）超位错（super-dislocation）堆垛层错（stacking fault）弗兰克-纳巴罗回路（Frank-Nabarro circuit）部分为错或不全位错（partial dislocation）向错强度（disclination strength）内禀层错（intrinsic fault）条纹织构（schlieren texture）表面能(surface energy) 适配(matching)晶界(grain boundary) 共格晶界(coherent boundary)小角度晶界（low angle grain boundary）非共格晶界(incoherent boundary)大角度晶界（high angle grain boundary 晶界迁移率(grain boundary mobility)倾转晶界（tilt boundary）取向关系(orientation relationship)扭转晶界（twist boundary）气泡(gas babble)相界(phase boundary) 空洞(void)扩散不可逆过程（irreversible process）传质过程（mass transport）扩散（diffusion）扩散距离（diffusion distance）唯象系数（phenomenological coefficient）间隙机制（interstitial mechanism）挤列结构（crowdion configuration）哑铃结构（dumbbell split configuration）空位机制（vacancy mechanism）换位机制（exchange mechanism）扩散流量（flux）参考系（reference frame）实验参考系（laboratory reference frame）点阵参考系（lattice reference frame）菲克第一定律（Fick’s first law）菲克第二定律（Fick’s second law）扩散系数（diffusion coefficient）禀性扩散系数（intrinsic diffusion coefficient）互扩散系数（mutual diffusion coefficient）自扩散系数（self-diffusion coefficient）稳态扩散（steady state diffusion）Kirkendall 效应（Kirkendall effect）Matano 平面（Matano interface）热力学因子（thermodynamic factor）同位素（isotope）示踪物（tracer）扩散偶（diffusion couple）误差函数（error function）哑变量（dummy）数值方法（numerical method）有限差分（finite-difference）收敛性（convergence）截断误差（truncation error）舍入误差（round-off error）相关系数（correlation factor）高扩散率通道（high-diffusivity path）体扩散（volume diffusion）晶界扩散（grain boundary diffusion）位错扩散（dislocation diffusion）表面扩散（surface diffusion）迁移率（mobility）渗透率（permeability）凝固分配系数（partition coefficient）枝晶偏析（dendrite segregation）区域提纯（zone-refining）亚共晶合金（hypoeutectic alloy）胞晶的形成（cell formation）过共晶合金（hypereutectic alloy）胞状树枝晶（cellular dendrite）片状（lamellar）柱状树枝晶（columnar dendrite）棒状（rod-like）共晶凝固（eutectic solidification）共晶领域（eutectic colony）包晶凝固（peritectic solidification）伪共晶（pseudo-eutectic）偏析（segregation）离异共晶（divorced eutectic）熔焊（fusion welding）激冷区（chill zone）快速凝固（rapid solidification process）柱状晶区（columnar zone）连续铸造（continuous casting）等轴晶区（equiaxed zone）树枝状显微偏析（dendritic microsegregation）收缩晶区（shrinkage cavity）非平衡杠杆定律（non-equilibrium lever rule）疏松（porosity）组分过冷（constitutional supercooling）非金属夹杂物（non-metallic inclusion）胞状组织（cellular structure）熔池（weld pool）二次枝晶（secondary dendrite）混合区（composite region）一次支晶（primary dendrite）热影响区（heat-affected zone）。

机械英文名词

目录1机构学2极限与配合3疲劳强度4可靠性5振动与冲击6摩擦学7螺纹连接8轴上零件9键连接10销钉连接11联轴器12离合器13制动器14滑动轴承15滚动轴承16弹簧17传动一般18齿轮传动19传动装置20锥齿轮传动21谐波传动22蜗杆传动23带传动24链传动25其他零件1机构学机构学theory of mechanisms机构mechanism机器machine机械machinery构件link主动件driving link从动件driven运动副kinematic pair铰链连接hinge, pilot pin joint复合铰链compound hinges, multiple hinges运动链kinematic chain低副lower pair高副higher pair自由度degree of freedom虚约束redundant constraint, passive constraint 机构简图schematic diagram of mechanism机构运动简图kinematic diagram of mechanism 机构综合synthesis of mechanism机构运动学kinematics of mechanism速比velocity ratio of link传动比transmission ratio速度瞬心instantaneous center of velocity机械动力学dynamics of machinery驱动力driving force扰动力perturbed force工作阻力effective resistance静载荷static load动载荷dynamic load离心力centrifugal force作用力active force, applied force 反作用力reaction等效力equivalent force力矩moment力偶couple力偶矩moment of couple力平衡equilibrium扭矩torque, torsional moment等效力矩equivalent moment效率efficiency等效构件equivalent link等效质量equivalent mass转动惯量moment of inertia惯性积product of inertia极转动惯量polar moment of inertia回转半径radius of gyration飞轮flywheel调速器governor, speed regulator转子的静平衡static balance of rotor转子的动平衡dynamic balance of rotor 平衡质量balancing mass质径积mass-radius product连续系统continuous system离散系统discrete system变质量系统variable mass system连杆机构linkage mechanism连架杆side link曲柄crank连杆coupler, floating link摇杆rocker滑块slider导杆guide bar, guide linkTotal 16 Page 11Total 16 Page 12Total 16 Page 1390 face anglebevel gear with axes at right anglesangular bevel gearTotal 16 Page 14Total 16 Page 15Total 16 Page 16。

材料化学英文术语

材料化学英文专业术语Ch1Rare-earth 稀土doped 掺杂的modification 修饰structural 结构的structure 结构mechanical 机械的rigidity 刚性fatigue strength 疲劳力量toughness 韧性hardness 硬性critical 临界的novel 新奇的density 密度temperature 温度property 特性ferroelectric 铁电的dielectric 介电的Meissner effect 麦斯内效应lacquer 漆microwave 微波ceramic 陶瓷insulation 绝缘intrinsic 本征的steel 钢铁pottery 陶器bronze 青铜iron 铁器functional materials 功能材料acoustical 声学的optical 光学的，视觉的electric 电的magnetic 磁性的thermal 热的combination Bond 结合键inorganic material 无机材料composite 复合材料ferrous metal 黑色金属材料Non-ferrous metal 有色金属材料concrete 混凝土glass 玻璃elementary substance 元素物质,基本物质，初等物质metalloid 半金属non-stoichiometry 非化学计量学crystalline 晶体noncrystalline 非晶体defect 缺陷diagram 相图magnesium 镁aluminum 铝monoatomic 单原子的lattice 点阵，点群space group 空间群crystal structure 晶体结构short range order(SRO) 短程有序long range order (LRO)长程有序silica 二氧化硅SiO2silicate 硅酸盐predictable 可预言的repetitive 重复的Atom spacing 原子间距distribute 分布conservation of crystal plane angle 晶面角守恒anisotropy 各向异性isotropy 各向同性anisotropy of physical property 物理性能的各向异性transition 过渡state 状态meso 介观spatial 空间的molecule 分子periodic array周期排列macrocharacteristic 宏观特征Regular geometric morphology 规则几何外形geometric 几何学的morphology 形态学fixed melting point 固定熔点heat of combustion 燃烧热combustion 燃烧Mirror plane 镜面Axis of rotation 旋转轴center of symmetry 对称中心symmetry 对称point symmetry 点对称axis of inversion 反轴plane symmetry 面对称screw axis 螺旋轴glide plane 滑移面Fedorov(费多罗夫) space group 代数工具Laue and braggs X-ray diffraction 物理工具thermodynamic 热力学的repeating pattern 重复图案kinetic 动力学的reaction rate 反应速率potential barrier 势阱linear lattice 直线点阵constituent 成分Space lattice(3D) 空间点阵One lattice point 点阵点multi-primitive cell 复式初基胞或复单位primitive cell 初基胞或素单位primitive translation vector 初基矢量或素向量parallel translation group 平移群plane lattice 平面点阵inert 惰性的spatial arrangement 空间排列amorphous 无定形的geometric 几何的metastable 亚稳的thermodynamics 热力学kinetics 动力学hotspot 热点dielectric 介电的Meissner effect 迈斯纳效应toughness 韧性fatigue strength 脆性acoustical 声学的optical 光学的ferrous metal 黑色金属Nobel metal 贵金属metalloid 半金属concrete 混凝土ceramic 陶瓷的rubber 橡胶plastics 塑料adhesive 粘合剂coating 涂料aggregation 团聚integration 集成interplanar spacing 晶面间距unit cell 单胞primitive translation vector 初基矢量或素向量parallel translation group 平移群primitive cell 初基胞或素单位multiple-primitive cell 复式初基胞或复单位spiral chains 螺旋线helix（复数：helices）螺旋（螺旋物）。

LRR结构功能进化

N,,--IIlIIIIII
c
Platelet glycoprotein Iba (Human)
N
~
Connectin (Drosophila)
N
Trk (Human)
N
FTT'I N- - E l - I - I T ] "
Thyrotropin
receptor (Dog)
cytoplasm p34 ribosome-binding protein (Rat) cell exterior Internalin (Liateats
Bostjan Kobe and Johann Deisenhofer
St Vincent's Institute of Medical Research, Fitzroy, Australia and Howard Hughes Medical Institute and University of Texas Southwestern Medical Center at Dallas, USA
In this review, we will focus primarily on three topics: first, new members of the L R R superfanfily identified in the last year; second, the possible structural diversity of LRR-containing proteins; third, the functional implications of the newly available three-dimensional structure of the complex between RI and its ligand, RNase A [7"]. For other aspects of LRRs and LRR-containing proteins, the reader is encouraged to refer to our earlier review [4%

Singularity of the density of states in the two-dimensional Hubbard model from finite size

a r X i v :c o n d -m a t /9503139v 1 27 M a r 1995Singularity of the density of states in the two-dimensional Hubbard model from ﬁnitesize scaling of Yang-Lee zerosE.Abraham 1,I.M.Barbour 2,P.H.Cullen 1,E.G.Klepﬁsh 3,E.R.Pike 3and Sarben Sarkar 31Department of Physics,Heriot-Watt University,Edinburgh EH144AS,UK 2Department of Physics,University of Glasgow,Glasgow G128QQ,UK 3Department of Physics,King’s College London,London WC2R 2LS,UK(February 6,2008)A ﬁnite size scaling is applied to the Yang-Lee zeros of the grand canonical partition function for the 2-D Hubbard model in the complex chemical potential plane.The logarithmic scaling of the imaginary part of the zeros with the system size indicates a singular dependence of the carrier density on the chemical potential.Our analysis points to a second-order phase transition with critical exponent 12±1transition controlled by the chemical potential.As in order-disorder transitions,one would expect a symmetry breaking signalled by an order parameter.In this model,the particle-hole symmetry is broken by introducing an “external ﬁeld”which causes the particle density to be-come non-zero.Furthermore,the possibility of the free energy having a singularity at some ﬁnite value of the chemical potential is not excluded:in fact it can be a transition indicated by a divergence of the correlation length.A singularity of the free energy at ﬁnite “exter-nal ﬁeld”was found in ﬁnite-temperature lattice QCD by using theYang-Leeanalysisforthechiral phase tran-sition [14].A possible scenario for such a transition at ﬁnite chemical potential,is one in which the particle den-sity consists of two components derived from the regular and singular parts of the free energy.Since we are dealing with a grand canonical ensemble,the particle number can be calculated for a given chem-ical potential as opposed to constraining the chemical potential by a ﬁxed particle number.Hence the chem-ical potential can be thought of as an external ﬁeld for exploring the behaviour of the free energy.From the mi-croscopic point of view,the critical values of the chemical potential are associated with singularities of the density of states.Transitions related to the singularity of the density of states are known as Lifshitz transitions [15].In metals these transitions only take place at zero tem-perature,while at ﬁnite temperatures the singularities are rounded.However,for a small ratio of temperature to the deviation from the critical values of the chemical potential,the singularity can be traced even at ﬁnite tem-perature.Lifshitz transitions may result from topological changes of the Fermi surface,and may occur inside the Brillouin zone as well as on its boundaries [16].In the case of strongly correlated electron systems the shape of the Fermi surface is indeed aﬀected,which in turn may lead to an extension of the Lifshitz-type singularities into the ﬁnite-temperature regime.In relating the macroscopic quantity of the carrier den-sity to the density of quasiparticle states,we assumed the validity of a single particle excitation picture.Whether strong correlations completely distort this description is beyond the scope of the current study.However,the iden-tiﬁcation of the criticality using the Yang-Lee analysis,remains valid even if collective excitations prevail.The paper is organised as follows.In Section 2we out-line the essentials of the computational technique used to simulate the grand canonical partition function and present its expansion as a polynomial in the fugacity vari-able.In Section 3we present the Yang-Lee zeros of the partition function calculated on 62–102lattices and high-light their qualitative diﬀerences from the 42lattice.In Section 4we analyse the ﬁnite size scaling of the Yang-Lee zeros and compare it to the real-space renormaliza-tion group prediction for a second-order phase transition.Finally,in Section 5we present a summary of our resultsand an outlook for future work.II.SIMULATION ALGORITHM AND FUGACITY EXPANSION OF THE GRAND CANONICALPARTITION FUNCTIONThe model we are studying in this work is a two-dimensional single-band Hubbard HamiltonianˆH=−t <i,j>,σc †i,σc j,σ+U i n i +−12 −µi(n i ++n i −)(1)where the i,j denote the nearest neighbour spatial lat-tice sites,σis the spin degree of freedom and n iσis theelectron number operator c †iσc iσ.The constants t and U correspond to the hopping parameter and the on-site Coulomb repulsion respectively.The chemical potential µis introduced such that µ=0corresponds to half-ﬁlling,i.e.the actual chemical potential is shifted from µto µ−U412.(5)This transformation enables one to integrate out the fermionic degrees of freedom and the resulting partition function is written as an ensemble average of a product of two determinantsZ ={s i,l =±1}˜z = {s i,l =±1}det(M +)det(M −)(6)such thatM ±=I +P ± =I +n τ l =1B ±l(7)where the matrices B ±l are deﬁned asB ±l =e −(±dtV )e −dtK e dtµ(8)with V ij =δij s i,l and K ij =1if i,j are nearestneigh-boursand Kij=0otherwise.The matrices in (7)and (8)are of size (n x n y )×(n x n y ),corresponding to the spatial size of the lattice.The expectation value of a physical observable at chemical potential µ,<O >µ,is given by<O >µ=O ˜z (µ){s i,l =±1}˜z (µ,{s i,l })(9)where the sum over the conﬁgurations of Ising ﬁelds isdenoted by an integral.Since ˜z (µ)is not positive deﬁnite for Re(µ)=0we weight the ensemble of conﬁgurations by the absolute value of ˜z (µ)at some µ=µ0.Thus<O >µ= O ˜z (µ)˜z (µ)|˜z (µ0)|µ0|˜z (µ0)|µ0(10)The partition function Z (µ)is given byZ (µ)∝˜z (µ)N c˜z (µ0)|˜z (µ0)|×e µβ+e −µβ−e µ0β−e −µ0βn (16)When the average sign is near unity,it is safe to as-sume that the lattice conﬁgurations reﬂect accurately thequantum degrees of freedom.Following Blankenbecler et al.[1]the diagonal matrix elements of the equal-time Green’s operator G ±=(I +P ±)−1accurately describe the fermion density on a given conﬁguration.In this regime the adiabatic approximation,which is the basis of the ﬁnite-temperature algorithm,is valid.The situa-tion diﬀers strongly when the average sign becomes small.We are in this case sampling positive and negative ˜z (µ0)conﬁgurations with almost equal probability since the ac-ceptance criterion depends only on the absolute value of ˜z (µ0).In the simulations of the HSﬁelds the situation is dif-ferent from the case of fermions interacting with dynam-ical bosonﬁelds presented in Ref.[1].The auxilary HS ﬁelds do not have a kinetic energy term in the bosonic action which would suppress their rapidﬂuctuations and hence recover the adiabaticity.From the previous sim-ulations on a42lattice[3]we know that avoiding the sign problem,by updating at half-ﬁlling,results in high uncontrolledﬂuctuations of the expansion coeﬃcients for the statistical weight,thus severely limiting the range of validity of the expansion.It is therefore important to obtain the partition function for the widest range ofµ0 and observe the persistence of the hierarchy of the ex-pansion coeﬃcients of Z.An error analysis is required to establish the Gaussian distribution of the simulated observables.We present in the following section results of the bootstrap analysis[17]performed on our data for several values ofµ0.III.TEMPERATURE AND LATTICE-SIZEDEPENDENCE OF THE YANG-LEE ZEROS The simulations were performed in the intermediate on-site repulsion regime U=4t forβ=5,6,7.5on lat-tices42,62,82and forβ=5,6on a102lattice.The ex-pansion coeﬃcients given by eqn.(14)are obtained with relatively small errors and exhibit clear Gaussian distri-bution over the ensemble.This behaviour was recorded for a wide range ofµ0which makes our simulations reli-able in spite of the sign problem.In Fig.1(a-c)we present typical distributions of theﬁrst coeﬃcients correspond-ing to n=1−7in eqn.(14)(normalized with respect to the zeroth power coeﬃcient)forβ=5−7.5for diﬀer-entµ0.The coeﬃcients are obtained using the bootstrap method on over10000conﬁgurations forβ=5increasing to over30000forβ=7.5.In spite of diﬀerent values of the average sign in these simulations,the coeﬃcients of the expansion(16)indicate good correspondence between coeﬃcients obtained with diﬀerent values of the update chemical potentialµ0:the normalized coeﬃcients taken from diﬀerentµ0values and equal power of the expansion variable correspond within the statistical error estimated using the bootstrap analysis.(To compare these coeﬃ-cients we had to shift the expansion by2coshµ0β.)We also performed a bootstrap analysis of the zeros in theµplane which shows clear Gaussian distribution of their real and imaginary parts(see Fig.2).In addition, we observe overlapping results(i.e.same zeros)obtained with diﬀerent values ofµ0.The distribution of Yang-Lee zeros in the complexµ-plane is presented in Fig.3(a-c)for the zeros nearest to the real axis.We observe a gradual decrease of the imaginary part as the lattice size increases.The quantitative analysis of this behaviour is discussed in the next section.The critical domain can be identiﬁed by the behaviour of the density of Yang-Lee zeros’in the positive half-plane of the fugacity.We expect toﬁnd that this density is tem-perature and volume dependent as the system approaches the phase transition.If the temperature is much higher than the critical temperature,the zeros stay far from the positive real axis as it happens in the high-temperature limit of the one-dimensional Ising model(T c=0)in which,forβ=0,the points of singularity of the free energy lie at fugacity value−1.As the temperature de-creases we expect the zeros to migrate to the positive half-plane with their density,in this region,increasing with the system’s volume.Figures4(a-c)show the number N(θ)of zeros in the sector(0,θ)as a function of the angleθ.The zeros shown in theseﬁgures are those presented in Fig.3(a-c)in the chemical potential plane with other zeros lying further from the positive real half-axis added in.We included only the zeros having absolute value less than one which we are able to do because if y i is a zero in the fugacity plane,so is1/y i.The errors are shown where they were estimated using the bootstrap analysis(see Fig.2).Forβ=5,even for the largest simulated lattice102, all the zeros are in the negative half-plane.We notice a gradual movement of the pattern of the zeros towards the smallerθvalues with an increasing density of the zeros nearθ=πIV.FINITE SIZE SCALING AND THESINGULARITY OF THE DENSITY OF STATESAs a starting point for theﬁnite size analysis of theYang-Lee singularities we recall the scaling hypothesis forthe partition function singularities in the critical domain[11].Following this hypothesis,for a change of scale ofthe linear dimension LLL→−1),˜µ=(1−µT cδ(23)Following the real-space renormalization group treatmentof Ref.[11]and assuming that the change of scaleλisa continuous parameter,the exponentαθis related tothe critical exponentνof the correlation length asαθ=1ξ(θλ)=ξ(θ)αθwe obtain ξ∼|θ|−1|θ|ναµ)(26)where θλhas been scaled to ±1and ˜µλexpressed in terms of ˜µand θ.Diﬀerentiating this equation with respect to ˜µyields:<n >sing =(−θ)ν(d −αµ)∂F sing (X,Y )ν(d −αµ)singinto the ar-gument Y =˜µαµ(28)which deﬁnes the critical exponent 1αµin terms of the scaling exponent αµof the Yang-Lee zeros.Fig.5presents the scaling of the imaginary part of the µzeros for diﬀerent values of the temperature.The linear regression slope of the logarithm of the imaginary part of the zeros plotted against the logarithm of the inverse lin-ear dimension of the simulation volume,increases when the temperature decreases from β=5to β=6.The re-sults of β=7.5correspond to αµ=1.3within the errors of the zeros as the simulation volume increases from 62to 82.As it is seen from Fig.3,we can trace zeros with similar real part (Re (µ1)≈0.7which is also consistentwith the critical value of the chemical potential given in Ref.[22])as the lattice size increases,which allows us to examine only the scaling of the imaginary part.Table 1presents the values of αµand 1αµδ0.5±0.0560.5±0.21.3±0.3∂µ,as a function ofthe chemical potential on an 82lattice.The location of the peaks of the susceptibility,rounded by the ﬁnite size eﬀects,is in good agreement with the distribution of the real part of the Yang-Lee zeros in the complex µ-plane (see Fig.3)which is particularly evident in the β=7.5simulations (Fig.4(c)).The contribution of each zero to the susceptibility can be singled out by expressing the free energy as:F =2n x n yi =1(y −y i )(29)where y is the fugacity variable and y i is the correspond-ing zero of the partition function.The dotted lines on these plots correspond to the contribution of the nearby zeros while the full polynomial contribution is given by the solid lines.We see that the developing singularities are indeed governed by the zeros closest to the real axis.The sharpening of the singularity as the temperature de-creases is also in accordance with the dependence of the distribution of the zeros on the temperature.The singularities of the free energy and its derivative with respect to the chemical potential,can be related to the quasiparticle density of states.To do this we assume that single particle excitations accurately represent the spectrum of the system.The relationship between the average particle density and the density of states ρ(ω)is given by<n >=∞dω1dµ=ρsing (µ)∝1δ−1(32)and hence the rate of divergence of the density of states.As in the case of Lifshitz transitions the singularity of the particle number is rounded at ﬁnite temperature.However,for suﬃciently low temperatures,the singular-ity of the density of states remains manifest in the free energy,the average particle density,and particle suscep-tibility [15].The regular part of the density of states does not contribute to the criticality,so we can concentrate on the singular part only.Consider a behaviour of the typedensity of states diverging as the−1ρsing(ω)∝(ω−µc)1δ.(33)with the valueδfor the particle number governed by thedivergence of the density of states(at low temperatures)in spite of theﬁnite-temperature rounding of the singu-larity itself.This rounding of the singularity is indeedreﬂected in the diﬀerence between the values ofαµatβ=5andβ=6.V.DISCUSSION AND OUTLOOKWe note that in ourﬁnite size scaling analysis we donot include logarithmic corrections.In particular,thesecorrections may prove signiﬁcant when taking into ac-count the fact that we are dealing with a two-dimensionalsystem in which the pattern of the phase transition islikely to be of Kosterlitz-Thouless type[23].The loga-rithmic corrections to the scaling laws have been provenessential in a recent work of Kenna and Irving[24].In-clusion of these corrections would allow us to obtain thecritical exponents with higher accuracy.However,suchanalysis would require simulations on even larger lattices.The linearﬁts for the logarithmic scaling and the criti-cal exponents obtained,are to be viewed as approximatevalues reﬂecting the general behaviour of the Yang-Leezeros as the temperature and lattice size are varied.Al-though the bootstrap analysis provided us with accurateestimates of the statistical error on the values of the ex-pansion coeﬃcients and the Yang-Lee zeros,the smallnumber of zeros obtained with suﬃcient accuracy doesnot allow us to claim higher precision for the critical ex-ponents on the basis of more elaborateﬁttings of the scal-ing behaviour.Theﬁnite-size eﬀects may still be signiﬁ-cant,especially as the simulation temperature decreases,thus aﬀecting the scaling of the Yang-Lee zeros with thesystem rger lattice simulations will therefore berequired for an accurate evaluation of the critical expo-nent for the particle density and the density of states.Nevertheless,the onset of a singularity atﬁnite temper-ature,and its persistence as the lattice size increases,areevident.The estimate of the critical exponent for the diver-gence rate of the density of states of the quasiparticleexcitation spectrum is particularly relevant to the highT c superconductivity scenario based on the van Hove sin-gularities[25],[26],[27].It is emphasized in Ref.[25]thatthe logarithmic singularity of a two-dimensional electrongas can,due to electronic correlations,turn into a power-law divergence resulting in an extended saddle point atthe lattice momenta(π,0)and(0,π).In the case of the14.I.M.Barbour,A.J.Bell and E.G.Klepﬁsh,Nucl.Phys.B389,285(1993).15.I.M.Lifshitz,JETP38,1569(1960).16.A.A.Abrikosov,Fundamentals of the Theory ofMetals North-Holland(1988).17.P.Hall,The Bootstrap and Edgeworth expansion,Springer(1992).18.S.R.White et al.,Phys.Rev.B40,506(1989).19.J.E.Hirsch,Phys.Rev.B28,4059(1983).20.M.Suzuki,Prog.Theor.Phys.56,1454(1976).21.A.Moreo, D.Scalapino and E.Dagotto,Phys.Rev.B43,11442(1991).22.N.Furukawa and M.Imada,J.Phys.Soc.Japan61,3331(1992).23.J.Kosterlitz and D.Thouless,J.Phys.C6,1181(1973);J.Kosterlitz,J.Phys.C7,1046(1974).24.R.Kenna and A.C.Irving,unpublished.25.K.Gofron et al.,Phys.Rev.Lett.73,3302(1994).26.D.M.Newns,P.C.Pattnaik and C.C.Tsuei,Phys.Rev.B43,3075(1991);D.M.Newns et al.,Phys.Rev.Lett.24,1264(1992);D.M.Newns et al.,Phys.Rev.Lett.73,1264(1994).27.E.Dagotto,A.Nazarenko and A.Moreo,Phys.Rev.Lett.74,310(1995).28.A.A.Abrikosov,J.C.Campuzano and K.Gofron,Physica(Amsterdam)214C,73(1993).29.D.S.Dessau et al.,Phys.Rev.Lett.71,2781(1993);D.M.King et al.,Phys.Rev.Lett.73,3298(1994);P.Aebi et al.,Phys.Rev.Lett.72,2757(1994).30.E.Dagotto, A.Nazarenko and M.Boninsegni,Phys.Rev.Lett.73,728(1994).31.N.Bulut,D.J.Scalapino and S.R.White,Phys.Rev.Lett.73,748(1994).32.S.R.White,Phys.Rev.B44,4670(1991);M.Veki´c and S.R.White,Phys.Rev.B47,1160 (1993).33.C.E.Creﬃeld,E.G.Klepﬁsh,E.R.Pike and SarbenSarkar,unpublished.Figure CaptionsFigure1Bootstrap distribution of normalized coeﬃcients for ex-pansion(14)at diﬀerent update chemical potentialµ0for an82lattice.The corresponding power of expansion is indicated in the topﬁgure.(a)β=5,(b)β=6,(c)β=7.5.Figure2Bootstrap distributions for the Yang-Lee zeros in the complexµplane closest to the real axis.(a)102lat-tice atβ=5,(b)102lattice atβ=6,(c)82lattice at β=7.5.Figure3Yang-Lee zeros in the complexµplane closest to the real axis.(a)β=5,(b)β=6,(c)β=7.5.The correspond-ing lattice size is shown in the top right-hand corner. Figure4Angular distribution of the Yang-Lee zeros in the com-plex fugacity plane Error bars are drawn where esti-mated.(a)β=5,(b)β=6,(c)β=7.5.Figure5Scaling of the imaginary part ofµ1(Re(µ1)≈=0.7)as a function of lattice size.αm u indicates the theﬁt of the logarithmic scaling.Figure6Electronic susceptibility as a function of chemical poten-tial for an82lattice.The solid line represents the con-tribution of all the2n x n y zeros and the dotted line the contribution of the six zeros nearest to the real-µaxis.(a)β=5,(b)β=6,(c)β=7.5.。

数学专业英语词汇（D）

数学专业英语词汇(D)d integrable d可积d integral d积分d'alembert principle 达朗贝尔原理d'alembert ratio test 达朗贝尔比例试验法d'alembert solution 达朗贝尔解d'alembertian 达朗伯符;达郎贝尔算子damped harmonic oscillation 阻尼谐振动damped oscillation 阻尼振动damped vibration 阻尼振动damping 阻尼damping factor 阻尼因子dantzig van de panne method 但泽范德潘方法darboux tangent 达布切线darboux theorem 达布定理data 数据data processing 数据处理data storage 数据存储器data storage register 数据存储寄存器death process 死亡过程death rate 死亡率debugging 堤序deca 十decade 十个decade scaler 十进制计数器decagon 十边形decahedron 十面体decameter 十米decay curve 衰变曲线deci 分decidability 可判定性decile 十分位数decimal 十进位的decimal arithmetic 十进算术decimal binary conversion 十二进制变换decimal digit 十进制数字decimal expansion 十进制展开decimal fraction 十进小数decimal notation 十进制记数法decimal number 十进小数decimal number system 十进制decimal of many places 多位十进小数decimal part 小数部分decimal place 小数位decimal point 小数点decimal representation 十进制记数法decimal system 十进制decimal to binary conversion 十二进制变换decimetre 分米decision 判定decision domain 决策域decision function 判定函数decision problem 判定问题decision procedure 判定过程decision space 判定空间decision theory 决策论decision variable 决策变量decision vector 决策向量decisive 决定的declination 倾斜decoder 译码器decomposability 可分解性decomposable form 可分解形式decomposable matrix 可分解矩阵decomposable operator 可分解算子decompose 分解decomposition 分解decomposition field 分解域decomposition formula 分解公式decomposition group 分解群decomposition in a direct sum 直和分解decomposition into linear factors 线性因子分解decomposition into partial fractions 部分分数分解decomposition operator 分解算子decomposition principle 分解原理decomposition theorem 分解定理decrease 减少decreasing function 递减函数decrement 减量dedekind axiom 绰金公理dedekind completion 绰金完备化dedekind cut 绰金切断dedekind domain 绰金环dedekind ring 绰金环dedekind set 绰金集dedekind sum 绰金和deduce 演绎deducibility 可推断deduction 演绎法deductive method 演绎法deductive proof 演绎证明defect 靠defect indices 扛数defect of operators 算子的靠defect of spline 样条的筐defect relation 控系defect subspaces 坑空间defective number 靠defective value 康deferent 圆心轨迹deficiency 靠deficiency index 扛标deficient number 靠definability 可定义性definable 可定义的define 定义definiendum 被定义者definiens 定义者defining contrast 定义对比defining equation 定义方程defining field 定义域defining relations 定义关系definite 定的definite divergence 定发散definite integral 定积分definiteness 梅性definition by induction 用归纳法定义definition by transfinite induction 依超限归纳法的定义deflation 降阶deform 使变形deformable 可变形的deformation 变形deformation ratio 形变比率deformation retract 形变收缩核deformation retraction 形变收缩degeneracy 退化degeneracy operator 退化算子degenerate 退化degenerate case 退化情况degenerate core 简并核degenerate distribution 退化分布degenerate eigenvalue 退化本盏degenerate extreme point 退化极值点degenerate kernel 退化核degenerate parabolic equation 退化抛物型方程degenerate polyhedron 退化多面体degenerate set 退化集degenerate simplex 退化单形degeneration 退化degree 次数degree of a polynomial 多项式的次数degree of a representation 表示度degree of accuracy 精确度degree of an equation 方程式的次数degree of approximation 近似度degree of freedom 自由度degree of inseparability 不可分次数degree of mapping 映射度degree of stability 稳定度degree of symmetry 对称度del 倒三角形del operator 倒三角形delay 延迟delay equation 延滞方程delay line store 延迟线存储器delay time 延迟时间delete 删去deleted neighborhood 去心邻域deletion 删除delocalization 非局部化delta function 狄垃克函数deltoid 形曲线demarcation 划分界线demi continuous 半连续的demonstrate 证明论证demonstration 证明denominate number 庚denomination 名称denominator 分母denote 指示dense 稠密的dense in itself 自密的dense in itself set 自密集dense set 稠集dense subset 稠子集denseness 稠密性denseness of set 集的密度densimetry 密度测定density 密度density distribution 密度分布density function 密度函数density matrix 密度矩阵density of distribution 分布密度density of simultaneous distribution 联合分布密度density theorem 密度定理denumerability 可数性denumerable 可数的denumerable set 可数集denumeration 计算depend 依赖dependence 相关dependent 相关的dependent equations 相关方程组dependent variable 应变数dependent variate 应变量depression 降低depth line 深度线derivability 可微性derivable 可微的derivate 导出数derivation 微分derivative 导数derivative of a distribution 分布导数derivative of a vector 向量导数derivative of higher order 高阶导数derivative of n th order n阶导数derive 导出derived algebra 导出代数derived equation 导出方程derived function 导数derived functor 导函子derived graph 导出图derived rule of inference 推理的导出规则derived series 导出列derived set 推导集derived unit 导出单位derogatory matrix 减次阵descartes rule of signs 笛卡儿正负号规则descending central series 降中心列descending chain 降链descending chain condition 降链条件descending difference 前向差分descending induction 递减归纳descending order 递减次序descending power series 递减幂级数descent 下降descent method 下降法description 描述description operator 摹状算子descriptive form 描述形式descriptive function 描述形式descriptive geometry 画法几何descriptive set theory 描述集论descriptive statistics 描述统计学design 计划design of experiments 实验设计detached coefficients 分离系数determinant 行列式determinant of infinite order 无限行列式determinant of the coefficients 系数行列式determinant of the coefficients of a linear form 线性形式的系数行列式determinantal divisor 行列式因子determinantal equation 行列式方程determinate 一定的determinate automaton 确定性自动机determinate system 确定组determine 决定出determined system 确定组determining equation 决定方程determining factor 决定因素deterministic digital system 确定性数字系统deterministic optimization 确定性最优化deterministic process 确定过程deterministic programming 确定性最优化develop 展开developability 可展性developable 可展的developable function 可展函数developable surface 可展曲面development 展开development in power series 幂级数展开deviate 偏离deviation 偏差deviation from the mean 平均偏差diadic system 二进制数系diagnostic routine 诊断程序diagonal 对角线diagonal continued fraction 对角连分数diagonal dominancy 对角优势diagonal element 对角元素diagonal form 对角型diagonal map 对角映射diagonal matrix 对角阵diagonal method 对角线法diagonal morphism 对角射diagonal of a determinant 行列式的对角线diagonal of the face 面对角线diagonal point 对边点diagonal procedure 对角线法diagonal process 对角线法diagonal sequence 对角序列diagonal sum 矩阵的迹diagonal sum rule 对角求和规则diagonalizable matrix 可对角化矩阵diagonalization 对角线化diagonalize 对角化diagonally dominant matrix 对角占优矩阵diagram 图表diagram scheme 图解概型diameter 直径diameter of a circle 圆的直径diametric plane 径面diamond shaped 菱形的dichotomy 二分法diffeomorphic mapping 微分同胚映射diffeomorphism 微分同胚映射difference 差difference boundary value problem 差分边值问题difference differential equation 差分微分方程difference equation 差分方程difference group 差群difference method 差分法difference operator 差分算子difference product 差积difference quotient 均差difference schema 差分格式difference sequence 差数序列difference set 差集difference table 差分表different 共轭差积differentiability 可微性differentiable 可微的differentiable function 可微函数differentiable manifold of class c c类微分廖differential 微分differential algebra 微分代数differential analyzer 微分分析仪differential and integral calculus 微积分differential calculus 微分学differential circuit 微分电路differential coefficient 微分系数differential cross section 微分截面differential curve 微分曲线differential difference equation 差分微分方程differential equation 微分方程differential equation with delayed argument 延滞方程differential equation with deviating argument 偏差自变数微分方程differential equation with lag 滞后微分方程differential equation with separated variables 分离变数型微分方程differential expression 微分式differential form 微分形式differential form of the first kind 第一种微分形式differential game 微分对策differential geometry 微分几何学differential ideal 微分理想differential method 微分法differential of arc 微弧differential operator 微分算子differential parameter 微分参数differential quotient 微分系数differential ring 微分环differential scattering 微分散射截面differential topology 微分拓扑differentiate 微分differentiating circuit 微分电路differentiation 微分differentiation of a function 函数的微分法differentiation of implicit function 隐函数微分法differentiation operator 微分算子differentiation symbol 微分记号differentiation term by term 逐项微分differentiation theorem 微分定理differentiator 微分器diffraction 衍射diffraction angle 衍射角diffraction curve 衍射曲线diffraction disc 绕射盘diffusion 扩散diffusion coefficient 扩散系数diffusion constant 扩散常数diffusion equation 扩散方程diffusion process 扩散过程digamma function 双函数digit 数字digital 数字的digital computer 数字计算机digital control 数字控制digital differential analyzer 数字微分分析仪digital recorder 数字式自动记录器digital simulation 数据模拟digitize 计数化dihedral angle 二面角dihedral group 二面体群dihedron 二面体dilatation 单项变换dilated maximum principle 扩张极大值原理dilemma 二难推论dimension 量纲dimension theorem 维数定理dimension theory 维数论dimensional 量纲的dimensional analysis 维量分析dimensional equation 量纲方程dimensionality 量纲dimensionless 无量纲的dimensionless quantity 无因次量dimer 二聚物dimetric 二维的diophantine analysis 丢番图分析diophantine equation 丢番图方程diplohedron 扁方二十四面体dirac delta distribution 狄垃克函数dirac equation 狄拉克方程dirac measure 狄拉克测度direct 直接的direct analytic continuation 直接解析开拓direct correspondence 直接对应direct decomposition 直分解direct factor 直积因子direct image 直接象direct limit 归纳极限direct method 直接法direct numerical method 直接数值法direct predecessor 直前仟direct product 直积direct successor 紧接后元direct sum 直和direct system 归纳系direct union 直并directed circuit 有向回路directed distance 有向距离directed edge sequence 有向棱序列directed graph 有向图directed group 有向群directed line 有向元directed line segment 有向线段directed path 有向通路directed quantity 有向量directed set 有向集directed system 有向系directing curve 有向曲线direction 方向direction angle 方向角direction cosine 方向余弦direction field 方向场direction of principal axis 轴方向direction of principal curvature 助率方向direction parameter 方向参数directional 定向的directional derivative 方向导数directional differentiation 方向微分法directional field 方向场directivity 方向性directly proportional 直接比例的directoin search program 方向检颂序director circle 准圆director cone 准锥面director plane 准平面directrix 准线directrix of a conic 二次曲线的准线dirichlet boundary condition 狄利克雷边界条件dirichlet conditions 狄利克雷条件dirichlet distribution 狄利克雷分布dirichlet domain 狄利克雷域dirichlet drawer principle 狄利克雷抽屉原理dirichlet function 狄利克雷函数dirichlet integral 狄利克雷积分dirichlet principle 狄利克雷原理dirichlet problem 狄利克雷问题dirichlet product 狄利克雷乘积dirichlet series 狄利克雷级数dirichlet space 狄利克雷空间dirichlet theorem 狄利克雷定理disagreement 不符合disappearance 消失disassembly 拆卸disc 圆盘disconnected space 不连通空间discontinuity 不连续discontinuity interval 不连续区间discontinuity on the left 左方不连续性discontinuity on the right 右方不连续性discontinuous function 不连续函数discontinuous group 不连续群discontinuous random variable 不连续变量discontinuous set 不连续集discontinuous term 不连续项discontinuous variate 不连续变量discontinuum 密断统discount 折扣discount factor 折扣因子discrete 分立的discrete category 离散范畴discrete continuous system 离散连续系统discrete distribution 离散分布discrete distribution function 离散分布函数discrete flow 离散流discrete fourier transform 离散傅里叶变换discrete group 离散群discrete mathematics 离散数学discrete optimization 离散最佳化discrete optimization problem 离散最优化问题discrete problem 离散问题discrete process 离散随机过程discrete programming 离散规划discrete random variable 离散随机变量discrete series 离散序列discrete set 离散集discrete spectrum 离散谱discrete state 离散状态discrete system 离散系统discrete time 离散时间discrete topological space 离散拓扑空间discrete topology 离散拓扑discrete uniform distribution 离散均匀分布discrete valuation 离散赋值discreteness 离散性discretization 离散化discretization error 离散化误差discrimator 判别式函数discriminant 判别式discriminant analysis 判别分析discriminant function 判别式函数discriminant of a polynomial 多项式的判别式discriminatory analysis 判别分析disjoint elements 不相交元素disjoint relations 不相交关系disjoint sets 不相交集disjoint sum 不相交并集disjoint union 不相交并集disjointed set 不相交集disjunction 析取disjunction sign 析取记号disjunction symbol 析取记号disjunctive normal form 析取范式disjunctive proposition 选言命题disk 圆盘disorder 无秩序disorder order transformation 无序有序变化dispersion 方差dispersion matrix 方差矩阵dispersion relations 分散关系dispersive 扩散的displacement 位移displacement operator 位移算符display statusconcomitant 相伴式disposition 配置disproportion 不相称disproportionate 不成比例的dissection 剖分dissimilar terms 不同类项dissipation 散逸dissipation of energy 消能dissipative function 散逸函数dissipative measurable transformation 散逸可测变换dissipative system 耗散系dissociation 解离dissociation constant 分离常数distance axioms 距离公理distance between two points 两点间距distance circle 距离圆distance function 距离函数distance matrix 距离矩阵distance meter 测距仪distance point 距离点distinction 差别distinguish 辨别distinguished polynomial 特异多项式distortion 畸变distortion angle 畸变角distortion theorem 畸变定理distortionless 无畸变的distributed constant 分布常数distributed parameter 分布参数distribution 分布distribution coefficient 分布系数distribution curve 分布曲线distribution family 分布族distribution function 分布函数distribution law 分布律distribution of prime numbers 素数分布distribution parameter 分布参数distribution ratio 分布系数distribution rule 分布规则distribution space 广义函数空间distribution with negative skewness 负偏斜分布distribution with positive skewness 正偏斜分布distributionfree test 无分布检验distributive 分配的distributive lattice 分配格distributive law 分配律distributivity 分配性disturbance 扰动disturbing function 扰动函数diverge 发散divergence 发散divergence of a series 级数发散divergence of tensor field 张量场的散度divergence of vector field 向量场的散度divergent sequence 发散序列divergent series 发散级数divide 除divided difference 均差dividend 被除数divider compasses 除法器两脚规dividers 除法器两脚规divisibility 可除性divisible 可除的divisible element 可除元素division 除法;划分division algebra 可除代数division algorithm 辗转相除法division of a line segment 线段的分割division ring 可除环division transformation 有剩余的除法division with remainder 有剩余的除法divisor 因divisor class 除子类divisor function 除数函数divisor problem 除数问题documentation 文件编制documentation of program 程序文档dodecagon 十二边形dodecagonal 十二边形的dodecahedral number 十二面体数dodecahedron 十二面体dog curve 追踪曲线domain 定义域domain of attraction 吸引范围domain of convergence 收敛域domain of definition 定义域domain of dependence 依赖域domain of existence 存在域domain of integration 积分区域domain of integrity 整环domain of meromorphy 亚纯域domain of regularity 正则域domain of transitivity 可递域domain of unsolvability 不可解域domain of variability 定义域dominant 帜dominant strategy 优策略dominant weight 最高权dominate 支配dominated convergence 控制收敛dominating set 控制集domination 支配domination principle 优势原理domino problem 多米诺问题dot 点dot chart 点图表dot product 纯量积dotted 点线的dotted line 点线dotted spinor 有点旋量double 双的double angle formulas 倍角公式double chain complex 双链复形double complex 二重复形double cone 对顶锥double coset 重倍集double cusp 双尖点double element 二重元素double exponential distribution 二重指数分布double folium 双叶线double fourier series 二重傅里叶级数double integral 二重积分double laplace transformation 二重拉普拉斯变换double layer 双层double layer potential 双层位势double limit 二重极限double line 二重线double loop 双环路double negation 双重否定double orthogonal system 二重正交系double periodicity 双周期性double plane 二重面double point 重点double point of curve 曲线的二重点double poisson distribution 二重泊松分布double product 二重积double ratio 交比double root 重根double sequence 二重数列double series 二重级数double subscript 双下标double sum 二重和double tangent 二重切线double valued function 双值函数double vector product 二重向量积doubly periodic function 双周期函数dozen 一打draw 拉drum 磁鼓dual abelian variety 对偶阿贝耳簇dual automorphism 逆自同构dual base 对偶基dual basis 对偶基dual category 对偶范畴dual cell 对偶胞腔dual complex 对偶复形dual cone 对偶锥dual curve 对偶曲线dual figure 对偶图dual form 对偶形式dual formula 对偶公式dual graph 对偶图dual group 特贞群dual ideal 对偶理想dual isomorphism 对偶同构dual lattice 对偶格dual mapping 对偶映射dual module 对偶模dual number 对偶数dual operation 对偶运算dual operator 对偶算子dual problem 对偶问题dual relation 对偶关系dual representation 对偶表示dual simplex method 对偶单形法dual spaces 对偶空间dual system 对偶系统dual theorem 对偶定理dual vector space 对偶向量空间duality 对偶性duality principle 对偶原理duality relation 对偶关系duality theorem 对偶定理duel 竞赛dummy index 哑指标duodecimal notation 十二进记数法duodecimal system 十二进制duodecimal system of numbers 十二进数系duplication formula 倍角公式duplication of the cube 倍立方duration 持久时间dyad 并向量dyadic expansion 二进展开dyadic product 并向量积dyadic rational 二进有理数dynamic optimization 动态最优化dynamic programming 动态规划dynamic store 动态存储器dynamic system 动力系统dynamical variables 动态变数dynamics 力学dynkin diagram 丹金图形。

物理专业词汇S2

specific binding energy 比结合能
specific conductance 导电率
specific electronic charge 电子的比电荷
specific gravity 比重
specific gravity bottle 比重瓶
specific heat 比热
spectroscopic parallax 分光视差
spectroscopic photography 分光摄影术
spectroscopy 光谱学
spectrum 光谱
spectrum locus 光谱轨迹
spectrum selector 光谱选挥器
spectrum variable 光谱变星
source of light 光源
source of sound 声源
south pole 南极
space 空间
space astronomy 空间天文学
space charge 空间电荷
space charge density 空间电荷密度
space charge effect 空间电荷效应
spectrohelioscope 太阳光谱观测镜
spectrometer 光谱仪
spectrometry 光谱测定法
spectrophotofluorometer 荧光分光光度计
spectrophotography 光谱摄影学
spectrophotometer 分光光度计
spectrophotometry 光谱测定法
spark chamber 火花室
spark counter 火花计数器

hypermesh面板命令一览表(中英文)

Hypermesh 命令一览表（上）Geom主面板 (3)Nodes子面板/Distance子界面 (3)Node edit 子界面 (3)Line edit子面板 (4)Lines子面板 (4)Defeature 子界面 (4)Circles 子界面 (4)Surfaces子界面/Surface edit子界面 (5)Midsurface 子界面 (6)Solids 子界面 (6)Solid edit 子界面 (7)Primitives 子界面 (7)Edge edit 子界面/ Point edit 子界面 (8)Auto cleanup 子界面 (9)Quick edit 子界面 (9)1D主面板 (9)Masses 子界面/Shp 子界面 (10)Rigids 子界面 (10)Fe joints 子界面 (10)Bars 子界面 (10)Connectors 子界面 (10)Spotweld 子界面 (13)Hyperbeam 子界面 (13)Line mesh 子界面/Vectors 子界面 (13)Systems 子界面 (14)Edit element 子单元 (14)Split 子单元 (14)Replace子单元/Detach子单元 (14)2D主面板 (14)Cones 子界面 (15)Planes 子界面 (15)Spheres 子界面 (15)Torus 子界面 (15)Drag 子界面 (16)Spin 子界面 (16)Elem offset 子界面 (16)Auto mesh 子界面 (16)Composites子界面 (17)Shrink wrap 子界面 (17)Smooth 子界面 (17)Quality index 子界面 (17)Elem cleanup 子界面 (17)3D 主面板 (18)Solid map 子界面 (18)Linear solid子界面/ Solid mesh 子菜单 (18)Tetramesh子界面 (19)Geom 主面板Nodes 节点Lines 线Surface 曲面Solid 实体Quick edit 快速编辑Node edit 节点编辑Line edit 线编辑Surface edit 曲面编辑Solid edit 实体编辑Edge edit 边编辑Temp nodes 临时节点Circles 圆Defeature简化几何模型Primitives 基本体Point edit 点编辑Distance 距离Length 长度Midsurface 中间面Auto clean up 自动清理Nodes 子面板 Distance 子界面Node edit 子界面Lineedit 子面板Create node 创造节点Create point 创造点 Type in 输入Reject 取消Pick geom.在几何体上建点Number of nodes 节点个数On line 在线上建点Bias intensity 偏置At point 在点上建立节点Number of nodes 建立几个节点Between 两点之间Bias intensity 偏置On plane 在面上建立节点Distance 距离Xdist X 方向的距离Ydist Y 方向的距离Zdist Z 方向的距离Angle节点之间的角度Two nodes 两个节点的距离Nodes between 两点之间放置几个节点Three nodes 三个节点Circle center圆心Two points 两个点的距离Three points 三个点Associate关联Tolerance 公差Move node 移动节点Step size移动尺寸大小Destination surf目标曲面Place node 放置节点Node to place节点到另一个地方Remap 重映射Node list 节点目录Align node 对齐节点Combine 合并Smooth 光滑Split at point指定点分割Split at joint 在连接处分割Split at line 用线分割Cut line剪切线Split at plane 用面分割Lines 子面板DDefeature 子界面Circles 子界面Circle 圆Radius 半径Center & radius 圆心& 半径Offset 偏移量Points & vector 点 & 向量Three points 三个点Find center 寻找中心Smooth corners 平滑转角Smooth line 使线光滑Min tangent angel最小切线角度Extend line 延长线Follow curvature 原有曲率From nodes 通过节点Linear 线性的Offset 偏移Offset by midline 通过中线偏移From surf edges 曲面边缘偏移Original component 偏移到原始组件里Ignore element normal 忽略法向单元Break angle 打断角度From features 通过特性选取Feature angle 特性角度Surfs with plane 面上的曲面Elements with plane 面上的单元Line with plane 面上的线At intersection 交集处Smooth lines 光滑线At tangent 切线Check points 检查点Radius 半径Fillets 圆角Trim original lines 修剪线段Pinholes 小孔Surf fillets 曲面倒角Diameter 直径Find fillets by profile 通过轮廓选取倒角Surf fillets 曲面倒角Find fillets in selected 在选择的部分选取倒角Edge fillets 边倒角Trim-intersect 修剪相交Duplicates 复制Cleanup tolerance 清除公差Find symmetry 寻找对称Reorganize 重组Delete positive 删除当前Symmetry 对称面Delete negative 删除复制体Surfaces 子界面Surface edit 子界面Multiple node 多个节点Trim with nodes 通过节点修剪Node normal to edge 矢量节点到边界Along a vector 沿着矢量Entire surface 全部的曲面Keep line Endpoints 保持线的终点Trim with lines 通过线修剪All attached surface 所有接触面With plane 用平面With surfs 用曲面Trim with surfs/plane 用曲面/平面修剪Self intersecting surfs自定义曲面At cursor 手动选取All trim lines of surfs所有曲面上的修剪线Untrim 还原修剪Internal trim lines 内部修剪线Disjoint offset 部分偏移Offset 偏移Remove degenerations 移除Cross Extension 同过延伸使交叉ExtendExtend selected surf edges延伸选择的曲面边界Shrink 缩放Ruled 规则面Auto reverse自动翻转Spline /filler样条线 / 填充线Auto create （free edges only ）自动创建（自由边）Skin 蒙皮Keep tangency 相切Drag along vector 沿着矢量拉伸Drag / spin 拉伸 / 旋转Drag along line 沿着线拉伸Auto detect features 自动检查特性Mesh-based auto tolerance网格自动调整公差Surface complexity 曲面复杂度Split by components 通过组件分割From FE 通过单元Associate nodes 关联节点auto select whole edge自动选择整个边界Pick angel 拾取角度Fillets 圆角Radius 角度Midsurface 子界面Solids 子界面Closed solid 闭合实体Extract 抽取Auto midsurface 自动抽取中间面Extraction options 提取选项Sort 分类Combine with adjacent plates连接与之相邻的板Combine all adjacent plates 连接所有相邻的板Surface pair 配对曲面Result in middle surface comp结果保存在中面组件中Target type 目标样式Point to offset 指定偏移量Quick edit 快速编辑Target location 目标位置Pilot pointPoint to offset 指定偏移量Accept target 接受目标Assign target 赋值目标Pilot pointRemove target 移除目标Retained edge 要保留的边缘Replace edge 替代边缘Edge to move 要移动的边界Extend surface 延伸曲面Surfaces to extend 延长曲面Max extension distension 最大移动距离View thickness 查看厚度Show surfaces thickness 观察曲面厚度Set thickness 设置厚度Auto select solid surfaces 自动选择实体曲面Bounding surfs 曲面边界Surfs component 保存到曲面组件中Drag along vector 沿着向量拖动Merge solids at shared edges 合并重合实体边界Drag along normal 沿着法向拖动Frame mode 框架模式Reference node 参照节点Drag along line 沿着线拖动Transformation planeSolid edit 子界面Primitives 子界面变换平面Spin 旋转Trim with nodes 通过节点修剪Extend trimmer 延伸修剪With cut line 通过剖切线With bounding lines通过边界线Drag a cut line 手动画剖切线With sweep lines 通过扫率曲线Trim with lines线修剪Sweep to 选择曲线Trim with plane/surf 平面/曲面修剪With plane 通过面With surfs 通过曲面To be merged 选取合并的实体Merge by removal 通过分割面合并实体Merge 合并Remove scratches删除刮伤Detach 分离To Detach 要分离的实体Boolean 布尔运算Operating type 操作类型Operating 具体操作Square/block 正方形/块Full cone 整个圆锥Partial cone 部分圆锥Botton center 底面中心Botton center 底面中心Normal vector 法向量Normal vector 法向量Top radius 顶部半径Major vector 主向量Base radius 根部半径Start angle 起始角度Height 高度End angle 终止角度Cylinder/cone 圆柱体/圆锥Axis ratio 轴比率By center and radius 通过中心和半径For partial sphere部分球体Sphere For 4 nodes sphere 通过四点创建球体Theta begin 起始角度Edge edit 子界面Point edit 子界面Theta end 终止角度Phi begin 起始直径Phi end 终止直径Minor radius 内环半径Major center 外环中心Torus 圆环Major radius 外环半径Minor center 内环中心Add 增加At cursor 光标选取Suppress 废除Multiple points 多重边界Break angle 打断角度Replace 替代Move point 去除的点Retained point 保留的点Release 释放Points to edges 点投影到线Points to surfs 点投影到曲面Distance tolerance 距离公差Angle tolerance 角度公差Project 投影Internal points onto its surfs 内部点映射到曲面At cursor 光标选取Toggle 忽略Cleanup tolerance 公差Suppress 压缩Break angle 打断角度Move edge 要移动的边Replace 替代Retained edge 要保存的边Equiv across comps 通过组件合并Equivalence 合并Equiv free edges only仅合并自由边Unsplit 清除分割Multiple edges 混合边界Min radius 最小半径Max radius 最大半径Min angle 最小角度Edge fillets 边界倒角Trim-intersect 修剪相交Close orphan 关闭孤行Angle surfs 曲面角度Offset surfs 偏移曲面Min filletAuto cleanup 子界面Quick edit 子界面1D 主面板最小倒角Max fillet 最大倒角Angel vertex 顶点角度Shape ratio 形状比例Min edge 最小边缘Topology cleanup parameters 拓扑清理参数Use current parameters 使用当前参数Elements quality criteria 元素质量标准Use current criteria 使用当前标准Split surf-node通过节点分割曲面Adjust/set density 调整/创建密度Split surf-line通过节点和目标线分割曲面Replace point 合并点Washer split 偏置分割线Add/remove point 添加/删除点Unsplit surf 合并分割曲面Add point on line 在线上增加点Toggle edge 忽略自由边Release point 释放点Filler surf 曲面倒角Project point 投影点Delete surf 删除曲面Trim-intersect 切除相交Masses 集中质量Bars 梁单元Connectors 连接器Line mesh 线性网格Edit element 编辑单元Fe joint 铰单元Rods 杆单元Spotweld 点焊单元Linear 1d 一维线性Split 分割Sph 球Rigids 刚性单元Hyperbeam Hyper 梁Replace 替代Rbe3橡胶单元Detach 分离Springs 弹簧单元Order change 改变阶次Gaps 间隙单元Vectors 向量Config edit 配置编辑Systems 坐标系Elem types 单元类型Masses 子界面Shp 子界面Rigids 子界面Fe joints 子界面Bars 子界面Connectors 子界面Organize 管理Spot焊点Add links增加连接Compare比较Find 查询Bolt螺栓Unrealize不真实Quality质量Mask 隐藏Seam 缝焊Delete 删除Area 面连接Translate 移动Apply mass 施加质量Numbers 数量Fe absorb FE吸附Renumbers从编号二级子界面OrganizeCollectors 集合Dest component 目标组件Includes 包括Dest目标Mass质量Create创造Property属性Update 更新System系统Simple cubic简单的立方体Pitch边长Material density材质密度Create创建Independent固定点Dependent连接点Attach dependent nodes as a set连接独立的点做设置Dof自由度Connectivity连接性Switch转换Update更新Attach/detach set连接/分离设置Combine合并Combine rigids with合并刚性单元通过Joint type连接类型Create创造Orientation定位Update 更新Spherical 球形的Bar2二维梁Pins aBar3三维梁Orientation/offsets in basic 简单的定位/偏移Update 更新Offset a a 偏移二级子界面Mask 二级子界面find 二级子界面translate 二级子界面deleteGlobal system 坐标系统Magnitude 偏移量二级子界面renumberStart with 从~~开始Single 单个Increment by 增加到二级子界面spot Location 位置Mesh independent 独立网格Spot 焊点Connect what 与~连接Non-normal projection 非均匀投影Creat 创建Tolerance 公差No systems 无系统Realize 实现Add location nodes as line 增加位置节点产生线Spacing 间距End offset 末端偏移Edit 编辑Retain line 保持线二级子界面boltLocation 位置Hole diameter 孔直径Bolt 螺栓Connect what 与~连接Use dynamic vector 使用动态矢量Creat 创建Tolerance 公差Mask 隐藏Reverse显示与隐藏颠倒Reverse all所有都相反状态Mask not shown 隐藏不显示Unmask all 全部显示Unmask 取消隐藏Reject 放弃Find entities 查找对象Find attached 查找连接Attached to 连接到Between 两者之间Delete associated solids 删除相关的实体Delete entity 删除实体Delete associated elems 删除相关的单元Delete model 删除模型Realize 实现Elems to current comp 创建单元到当前组件中中二级子界面seam Location 位置Mesh independent 独立网格Seam 缝焊Connect with 与~连接Creat 创建Tolerance 公差Realize 实现Elems to current comp 创建单元到当前组件中Spacing 间距Params 参数End offset 末端偏移Edit 编辑Group 组Connect rule 连接规则二级子界面area Location 位置Mesh independent 独立网格Area 面Connect with 与~连接Non-normal projection 非均匀投影Creat 创建Tolerance 公差No systems 无系统Realize 实现Elems to current comp 创建单元到当前组件中Mapped type 映射类型Size and bias 尺寸和偏移量Edit 编辑Free type 自由样式Element size 单元尺寸二级子界面Apply mass二级子界面Add links Location 位置Add links 增加连接Connect when 连接时间Connect what 与~~连接Re-connect rule 重新连接的规则Location 位置Mass type 网格类型Connect method 连接方法Distribution 分布Connect what 与~~连接Search tolerance 查询公差二级子界面QualitySpotweld 子界面Hyperbeam 子界面Merge tolerance 合并公差Cross section plane 通过界面Create node at centroid 创建节点在图心Plane base node 平面基准点Shell section 壳截面Create node at shear center 创建节点在剪切中心Part generation 产生部分Solid section 实体截面Analysis type 分析类型Standard section 标准截面Standarad section library 标准截面数据库Standarad section type 标准截面形式Generic section 普通截面Edit section 编辑截面Plot centroid 显示型心Review sections 审查截面Shear center 切变中心Line mesh 子界面Vectors 子界面Preview duplicates 预览重复单元Preview combine 预览合并Connectors 连接Remove duplicates 移除重复单元Projection check 投影校核Find too long 寻找太长的1D elems 1D 单元Length 长度Angle 角度3D elems 3D 单元Jacobian 雅克比All surfs 所有曲面Element config 单元配置Using geom.使用几何Weld location 焊接位置Using nodes 使用节点Without systems 无系统Using elems 使用单元Attach to shell elems 附在壳上的单元Switch nodes 转换节点Element size 单元格大小Segment is whole line 整个线段分段Peoperty 性质Element config 单元配置Vector update method 矢量修正方法Create 创建Magnitude 量Update 更新Global system 坐标系统Systems 子界面Edit element 子单元Split 子单元Replace子单元Detach子单元2D主面板Planes 平面Ruled规则面Connectors连接器Automesh自动划分网格Edit element编辑单元Cones 圆锥Spline样条线HyperlaminateHyper薄板Shrink wrap收缩翘曲Split分割Spheres 球体Skin三角形Composites复合材料Smooth光滑Replace替代Torus 圆环Drag拉伸Qualityindex质量指标Detach分离Create by axis direction 通过轴方向创建create by node reference通过参照节点创建Rectangular 矩形Set reference 设置参考Assign赋值Set displacement设置位移Material orientation 定义材料Material orientationalmethod定义材料方法Plot绘图Tria三角形Quad正方形Tetra四面体Pyramid棱锥Penta五面体Create创建Hex六面体Combine合并Combine to quad合并成正方体Split分割Displayed elems显示单元Cleanup清理Plate elements 板单元Split all sides 分割所有的边Solid elements 实体单元Split into hexas 分割成六面体Hexa elements 六面体单元Two pentas二个五边形Refine to target element size 改善目标单元的尺寸Refine elements改善单元体Target element edge length目标单元边界长度Replace 移动的点Equivalent 等价With不动的点At mid-point在混合节点Detach分离Detach elements分离单元Detach from从~中分离Spin 旋转Elem cleanup 单元清理Order change 改变阶次Line drag 拉伸Config edit 配置编辑Elem offset 单元偏置Elem types 单元类型Cones 子界面Botton center 底面中心Mesh, keep surf划分网格，保留曲面Normal vector 法向量Radius 半径Top radius 顶部半径Ratio 比率Full cone 完整的圆锥Height 高度Major radius 外环半径Start angle 起始角User controlled 自定义Cone 圆锥End angle 终止角Planes 子界面Spheres 子界面Torus 子界面Mesh, keep surf划分网格 , 保留曲面Trimmed 修剪Calculate plane 估算面Square 正方形Full sphere 整个球Mesh, keep surf 划分网格，保留曲面Four points 四个点画球Radius 半径Theta begin 起始角度Theta end 终止角度Phi begin 起始直径User controlled 自定义Phi end 终止直径Center 中心Mesh, keep surf 划分网格，保留曲面Full torus 整个圆环Normal vector 法向量Minor radius 内环半径User controlledMajor vector 主向量Major radius 外环半径Drag 子界面Spin 子界面Elem offset 子界面Connectors 子界面参照1D Connectors Auto mesh 子界面Minor start 内环起始角Major center 外环中心Minor end 内环结束角Minor center 内环中心Major start 外环起始角Three points 三点确定Minor radius 内环半径Major end 外环结束角Distance 距离Drag geoms 拉伸几何体Mesh, keep surf 划分网格，保留曲面Bias style 偏载类型Drag elems 拉伸单元Bias intensity 偏载强度Angle 角度Spin geoms 旋转几何体Mesh, keep surf 划分网格，保留曲面On spin Bias style 偏载类型Spin elems 旋转单元Bias intensity 偏载强度Number of layer 层的数量Solid layers 实体层Initial offset 初始偏移量Tolal thickness 总体厚度Shell layers 壳层Elems to offset 单元偏移Linear or no biasing 线性或不偏载Bias intensity 偏载强度Shell offset 壳偏移量Elements to current comp 创建创建单元到当前组件中CFD corners CFD 角Thicken shells 加厚壳Along geom to follow 沿着几何偏移Shells are on the midsurfaces壳加在中间层Elements size 单元尺寸Elems to surf component 创建单元到面组件Composites 子界面Shrink wrap 子界面Smooth 子界面Quality index 子界面Elem cleanup 子界面Mesh type 单元类型First order 一阶Break connectivity 打断当前连接Previous settings 先前的设置Link opposite edges 连接对面的边QI optimize QI 优化Use current criteria 使用当前条件Smooth across common edges with feature angle光滑有特性角度的共同边Min elem size 最小单元尺寸Edge deviation 边界偏差Max elem size 最大单元尺寸Max angle 最大角度Closed volume proximity封闭附近的体积Surface deviation曲面偏差Mesh type 网格形式Free edge deviation 自由边的偏差Rigid body mesh 刚性体网格Max feature ang 最大的特性角度Material orientation 指定材料Material orientational method 指定材料方法Ply directions厚度方向Tight 紧的Element size 单元尺寸Loose 松散的Generate solid mesh 产生实体网格Mesh orientation 网格方向Iteration 迭代次数Plates 板AnchorSolids 实体Autodecide 自动决定Min size 最小尺寸Place node 放置节点Max size 最大尺寸Swap edge 交换边界Aspect ratio 长宽比Node optimize 节点优化Warpage 翘曲Element optimize 单元优化Skew 扭曲度Jacobian 雅克比Fix folded elems ，angles 修复折叠的单元，角Use surrounding elems 使用周围的单元Reduce tria elems 减少三角单元Use current criteria 使用现有标准QI smooth elems with target QI 光滑单元的目标Feature angle 特征角Fix elems failing QI check 修复单元QI 故障检查Edit element、split、replace、detach参照1D 3D 主面板Solid map 实体映射Drag拉伸Connectors链接Tetramesh四面体格划分Edit element编辑单元Linear solid 线性实体Spin旋转Smooth光滑Split分割Solid mesh 实体网格Line drag拉伸Replace替代Elem offset单元偏置Detach分离Order change改变阶次Config edit配置编辑Elem types单元类型Solid map 子界面Source geom 起始几何Along parameters 参数设置Dest geom 目标几何体Along bias style 偏置形式General 普遍方法Along geom 沿着几何体Elem size 单元尺寸Line drag沿着线拉伸Show solidmap mesh显示实体网格Linear线性Linear solid 线性实体Apply orthogonality to along 相交延长Ends only 终止处One volume 一个实体Smooth dest目标光滑Interactive互动Stop meshing on bad jacobian在不好的雅可比处停止划分网格Multi solids 混合实体Source shell 壳源Previous setting 先前的设置Linear solid子界面Solid mesh 子菜单Alignment 对齐方式Distribute layer 分布的层Density 密度Bais intensity偏载强度Start region开始区域End region结束区域Connecting连接Uniform mesh统一的网格Drag 、Spin 、Line drag 、Elem offset 、Connectors 参照2DTetramesh 子界面Select trias/quads to tetra mesh 选择三面体/四面体进行四面体网格自动划分Optimize mesh quality 优化网格质量Tetra mesh 四面体网格No fixed trias/quads 不修复三面体/四面体Standard 标准Tetra remesh四面体网格重新自动划分Fixed with boundary layer 修复边界网格Number of layers 层的数量Comps 组件First layer thickness 第一层的厚度Single thickness 单一厚度Growth rate 增长率Float w/o boundary layer 浮动w/o 边界层Simple transition ：ratio 单个旋转比CFD mesh CFD 网格Remesh重新划分网格Enclose volume 闭合的实体Volume tetra 四面体体积Match existing mesh 匹配存在的网格Elems to current comp 创建单元到当前组件中Smooth 参照2D。

计量经济学中英文词汇对照

Common variance Common variation Communality variance Comparability Comparison of bathes Comparison value Compartment model Compassion Complement of an event Complete association Complete dissociation Complete statistics Completely randomized design Composite event Composite events Concavity Conditional expectation Conditional likelihood Conditional probability Conditionally linear Confidence interval Confidence limit Confidence lower limit Confidence upper limit Confirmatory Factor Analysis Confirmatory research Confounding factor Conjoint Consistency Consistency check Consistent asymptotically normal estimate Consistent estimate Constrained nonlinear regression Constraint Contaminated distribution Contaminated Gausssian Contaminated normal distribution Contamination Contamination model Contingency table Contour Contribution rate Control

Phenix-refinement

coordinates, B-values, occupancies minimization, simulated annealing Function based on electron density (real-space reﬁnement) Function based on structure factors (reciprocal-space reﬁnement)
Reducing Overﬁtting in Reﬁnement
• • • •
• • • • • • •
Cross-validation
Brunger, Nature 355, 472, 1992 Rice & Brunger, Proteins 19, 277, 1994 Winn et al., Acta Cryst. D 57, 122-133, 2001 Bricogne, Meth. Enzymol. 276, 361, 1997 Murshudov, Dodson,Vagin, CCP4, 1996 Pannu & Read, Acta Cryst. A 52, 659-668, 1996 Adams, Pannu, Read, Brunger, PNAS 94, 5018, 1997
E ADP
(U
i
" Uj )
2
# Ui + U j & average_power % ( $ 2 '
Constraints
• • •
• • • • • • • •
Rigid-body reﬁnement
For example, molecule consists of two domains, only reﬁne position and orientation of each domain uses only 2 * (3 rotational + 3 translation) = 12 parameters So few parameters it requires only low-resolution data Torsion angle reﬁnement All atoms have the same B one parameter All main-chain and all side-chain atoms in each residue have the same B one or two parameters per residue TLS reﬁnement 20 parameters per group A number of N NCS-related molecules/domains are assumed to be identical Reduces the number of parameters by a factor N

药物分析常用英语词汇

药物分析专业英语词汇表Aabsorbance吸收度absorbanceratio吸收度比值absorption吸收absorptioncurve吸收曲线absorptioncoefficient吸收系数accuratevalue准确值Acid—dyecolormcty酸性染料比色法acidimcty酸量法acidity酸度activity活度adjustedretentiontime调整保留时间absorbent吸收剂absorption吸附alkalinity碱度alumina氧化铝，矾土ambienttemperature室温ammoniumthiocyanate硫氰酸铵analyticalqualitycontrol分析质量控制anhydroussubstance 干燥品antioxidant抗氧剂applicationofsample点样areanormalizationmethod面积归一法arsenic砷arsenicsport砷斑assay含量测定assaytolerance含量限度attenuation衰减acidburette酸式滴定管alkaliburette碱式滴定管amortar研钵Bbackextraction反萃取bandabsorption谱带吸收batch批batchnumber批号Benttendorlfmethod白田道夫法betweendayprecision日间密度精biotransformation生物转化blanktest空白试验boilingrange沸程BritishPharmacopeia英国药典bromatetitration溴酸盐滴定法brominemethod溴量法bromothymolblue溴麝香酚蓝bulkdrug原料药by—product副产物breaker烧杯buretteglassbeadnozzle滴定管brownacidburette棕色酸式滴定管Ccalibrationcurve校正曲线calomelelectrode甘汞电极calorimetry量热分析capacityfactor容量因子capillarygaschromatography毛细管气相色谱法carriergas载气characteristicsdescription性状chelatecompound螯合物chemicalequivalent化学当量Chinesepharmacopeia中国药典Chinesematerialmedicine中成药Chinesematerialmidicalpreparation中药制剂chiral手性的chiralcarbonatom手性碳原子chromatogram色谱图chromatography色谱法chromatographiccolumn色谱柱chromatographiccondition色谱条件clarity澄清度coefficientofdistribution分配系数coefficientofvariation变异系数colorchangeinterval变色范围colorreaction显色反应colormetry比色法columnefficiency柱效columntemperature柱温comparativetest比较试验completenessofsolution溶液的澄清度conjugate缀合物concentration—timecurve浓度时间曲线confidenceinterval置信区间confidencelevel置信水平controlledtrial对照试验correlationcoefficient相关系数contrasttest对照试验congealingpoint凝点contentunifarmity装量差异controlledtrial对照试验correlationcoefficient相关系数contrasttest对照试验counterion反离子cresalred甲酚红cuvettecell比色池cyanide氰化物casserolesmall勺皿Ddead—stoptitration永定滴定法deadtime死时间deflection偏差deflectionpoint拐点degassing脱气deionizedwater去离子水deliquescence潮解depressorsubstancestest降压物质检查法desiccant干燥剂detection检查developingreagent展开剂developingchamber展开室deviation偏差dextrose右旋糖diastereoisomer非对映异构体diazotization重氮化differentialthermalanalysis差示热分析法differentialscanningcalorimetry差示扫描热法Gutzeit古蔡daytodayprecision日间精密度dissolution溶出度directinjection直接进样2,6-dichlorindophenoltitration2,6-二氯靛酚滴定法digestion消化diphastictitration双向滴定disintegrationtest崩解试验dispersion分散度dissolubility溶解度dissolutiontest溶解度检查distillingrange滴程distributionchromatography分配色谱dose剂量drugqualitycontrol药品质量控制dryingtoconstantweight干燥至恒重duplicatetest重复试验diskmethodwatermethod压片法Eeffectiveconstituent有效成分effectiveplatenumber有效板数effectiveofcolumn柱效electrophoresis电泳elimination消除eluate洗脱液elution洗脱enamtiomer对映体endabsorption末端吸收endogenoussubstances内源性物质enzymedrug酶类药物enzymeinduction酶诱导enzymeinhibition酶抑制epimer差向异构体equilibriumconstant平衡常数errorinvolumetricanalysis容量分析误差exclusionchromatography排阻色谱法expirationdate失效期externalstandardmethod外标法extract提取物extrationgravimetry提取重量法extractiontitration提取容量法extrapolatedmethod外插法Erlenmeyerflask锥形瓶evaporatingdishsmall蒸发皿elongatedbulb胖肚electronicbalanceMettlerAL204MettlerAL204电子天平Ffactor系数fehling’sreaction斐林实验filter过滤finenessoftheparticles颗粒细度flowrate流速fluorescentagent荧光剂fluorescencespectrophotometry荧光分光光度法fluorescencedetection荧光检测器fluorescenceanalysis荧光分析法foreignpigment有色杂质formulary处方集free游离freezingtest冻结试验fusedsilica熔融石英filterpaper滤纸Ggaschromatography气相色谱法gas-liquidchromatography气液色谱法gaspurifier气体净化器Generalidentificationtest一般鉴别试验generalnotices凡例Generalrequirements(药典)通则goodclinicalpractices药品临床管理规范goodlaboratorypractices药品实验室管理规范goodmanufacturingpractices(GMP)药品生产质量管理规范goodsupplypractices(GSP)药品供应管理规范gradientelution梯度洗脱grating光栅gravimetricmethod重量法Gutzeittest古蔡(检砷)法glassfunnellongstem玻璃漏斗gradcylinder量筒glassrod玻棒graduatedpipettes刻度吸管GC气相色谱Hheavymetal重金属halfpeakwidth平峰宽heatconductivity热导率heightequivalenttoatheoreticalplate理论塔板高度heightofaneffectiveplate有效塔板高度high-performanceliquidchromatography(HPLC)高效液相色谱法high-performancethin-layerchromatography(HPTLC)高效薄层色谱法hydrate水合物hydrolysis水解hydrophilicity亲水性hydrophobicity疏水性hydroxylvalue羟值hyperchromiceffect浓色效应hypochromiceffect淡色效应HHS-typeconstanttemperaturewaterbathHHS型恒温水锅HPLC高效液相色谱法Iidentification鉴别ignitiontoconstantweight灼烧至恒重immobilephase固定相immunoassay免疫测定impurity杂质inactivation失活index索引indicatorelectrode指示电极indicator指示剂inhibitor抑制剂injectingseptum进样隔膜胶垫instrumentalanalysis仪器分析injectionvalue进样阀insulinassay胰岛素生物检测法integrator积分仪intercept截距interface接口internalstandardsubstance内标物质Internationalunit国际单位invitro体外invivo体内iodide碘化物iodoformreation碘仿反应iodometry碘量法ionpairchromatography离子对色谱ionsuppression离子抑制ionsuppression离子抑制ionicstrength离子强度ion-pairingagent离子对试剂ionization电离isoabsorptivepoint等吸收点isocraticelution等溶剂组成洗脱isoelectricpoint等电点isoosmoticsolution等渗溶液irreversibleindicator不可逆指示剂irreversiblepotential不可逆电位KKarlFischertitration卡尔-费舍尔滴定Kjeldahlmethodfornitrogen凯氏定氮法Koberreagent 科伯试剂Kovatsretentionindex科瓦茨保留指数Llabelledamount标示量leadingpeak前延峰levelingeffect均化效应licensedpharmacist执业药师limitcontrol限量控制limitofdetection检测限limitofquantitation定量限limittest杂质限度试验lossondrying干燥失重lowpressuregradientpump氧压梯度泵linearityandrange线性及范围linearityscanning线性扫描luminescence发光litmuspaper石蕊试纸lyophilization冷冻干燥Mmainconstituent主成分make-upgas尾吹气maltolreaction麦芽酚试验Marquistest马奎斯试验massanalyzerdetector质量分析检测器massspectrometricanalysis质谱分析massspectrum质谱图meandeviation平均偏差meltingpoint熔点meltingrange熔距metabolite代谢物metastableion亚稳离子micellarchromatography胶束色谱法microanalysis微量分析microcrystal微晶microdialysis微透析migrationtime迁移时间Milliporefiltration微孔过滤mobilephase流动相molecularformula分子式monitor检测monochromator单色器monographs正文Nnaturalproduct天然产物Nessler’sreagent碱性碘化汞试液neutralization中和nitrogencontent总氮量nonaqueousacid-basetitration非水酸碱滴定nonprescriptiondrug,overthecounterdrugs非处方药nonspecificimpurity一般杂质non-volatilematter不挥发物normalphase正相normalization归一化法Nesslercolorcomparisontube纳氏比色管Onotice凡例octadecylsilanebondedsilicagel十八烷基硅烷键合硅胶odorless辛基硅烷odorless无臭officialname法定名officialtest法定试验on-columndetector柱上检测器on-columninjection柱头进样onthedriedbasis按干燥品计opalescence乳浊opticalactivity光学活性opticalisomerism旋光异构opticalpurity光学纯度organicvolatileimpurities有机挥发性杂质orthogonaltest正交试验orthophenanthroline邻二氮菲outlier可疑数据overtones倍频封oxidation-reductiontitration氧化还原滴定oxygenflaskcombustion氧瓶燃烧Ppackedcolumn填充柱packingmaterial色谱柱填料palladiumioncolorimetry钯离子比色法parention母离子particulatematter不溶性微粒partitioncoefficient分配系数patternrecognition(ppm)百万分之几peaksymmetry峰不对称性peakvalley峰谷peakwidthathalfheight半峰宽percenttransmittance透光百分率pHindicatorabsorbanceratiomethodpH指示剂吸光度比值法pharmaceuticalanalysis药物分析pharmacopeia药典pharmacy药学photometer光度计polarimetry旋光测定法polarity极性polydextrangel葡聚糖凝胶potentiometer电位计potentiometrictitration电位滴定法precipitationform沉淀形式precision精密度preparation制剂prescriptiondrug处方药pretreatment预处理primarystandard基准物质principalcomponentanalysis主成分分析prototypedrug原型药物purification纯化purity纯度pyrogen热原pycnometermethod比重瓶法plasticwashbottle洗瓶platformbalance天平pipette移液管pyknowmeterflasks容量瓶Qqualitycontrol质量控制qualityevaluation质量评价qualitystandard质量标准quantitativedetermination定量测定quantitativeanalysis定量分析quasi-molecularion准分子离子Rracemization消旋化randomsampling随机抽样rationaluseofdrug合理用药readilycarbonizablesubstance易炭化物质reagentsprayer试剂喷雾剂recovery回收率referenceelectrode参比电极relatedsubstance相关物质relativedensity相对密度relativeintensity相对强度repeatability重复性replicatedetermination平行测定reproducibility重现性residualbasichydrolysismethod剩余碱水解法residualliquidjunctionpotential残余液接电位residualtitration剩余滴定residuceonignition炽灼残渣resolution分辨率responsetime响应时间retention保留reversedphasechromatography反相色谱法reverseosmosis反渗透rinse淋洗robustness可靠性round修约reagentbottles试剂瓶roundbottomflask圆底烧瓶rubbersuctionbulb洗耳球Ssafety安全性Sakaguchitest坂口试验saltbridge盐桥saltingout盐析sampleapplicator点样器sampleapplication点样sampling取样saponificationvalue皂化值saturatedcalomelelectrode饱和甘汞电极selectivity选择性significantdifference显着性水平significanttesting显着性检验silicaget硅胶silverchlorideelectrode氯化银电极similarity相似性sodiumdodecylsulfate十二基酸钠solid-phaseextraction固相萃取solubility溶解度specificabsorbance吸收系数specification规格specificity专属性specificrotation比旋度specificweight比重spiked加入标准的splitinjection分流进样sprayreagent显色剂stability稳定性standardcolorsolution标准比色液standarddeviation标准差standardization标定standardsubstance标准品statisticalerror统计误差sterilitytest无菌试验stocksolution储备液stoichiometricpoint化学计量点storage贮藏straylight杂散光substrate底物substituent取代基sulfate硫酸盐sulphatedash硫酸盐灰分support载体suspension旋浊度swellingdegree膨胀度symmetryfactor对称因子systematicerror系统误差separatingfunnel分液漏斗stopcock玻璃活塞scissors剪刀spiritlamp酒精灯silicagelGthinlayer硅胶G薄层板Ttable片剂tailingfactor拖尾因子tailingpeak拖尾峰testsolution试液thermalanalysis热分析法thermalconductivitydetector热导检测器thermogravimetricanalysis热重分析法TheUnitedStatesPharmacopoeia美国药典ThePharmacopoeiaofJapan日本药局方thinlayerchromatography薄层色谱thiochromereaction硫色素反应thymol百里酚thymolphthalein百里酚酞titer滴定度three-dimensionalchromatogram三维色谱图titrant滴定剂titrationerror滴定误差titrimetricanalysis滴定分析法tolerance容许限totalash总灰分totalqualitycontrol全面质量控制traditionaldrugs传统药traditionalChinesemedicine中药turbidance浑浊turbidimetricassay浊度测定法turbidimetry比浊度turbidity浊度Uultracentrifugation超速离心ultravioletirradiation紫外线照射unduetoxicity异常毒性uniformdesign均匀设计uniformityofdosageunits含量均匀度uniformityofvolume装量均匀性uniformityofweight重量均匀性Vvalidity可靠性variance方差viscosity粘度volatileoildeterminationapparatus挥发油测定器volatilization挥发性volumetricanalysis容量分析volumetricsolution滴定液volumetricflasks比重瓶Wwavelength波长wavenumber波数weighingbottle称量瓶weighingform称量形式well-closedcontainer密闭容器whiteboard白瓷板XxylenecyanolblueFF二甲苯蓝FFxylenolorange二甲酚橙ZZigzagscanning锯齿扫描zwitterions两性离子Zymolysis酶解作用zoneelectrophoresis区带电泳。

comsol涡流模块.pdf

F = T n dS
∂Ω
The Force Calculation feature automatically performs the integral along the boundaries of the desired region, considering also the axisymmetric geometry of the problem. The computed force will be available in results processing as a global variable.
6
6 Click the Build All Objects button. The geometry is now complete.
Next, add the materials relevant to the model. MATERIALS On the Home toolbar, click Add Material. ADD MATERIAL 1 Go to the Add Material window. 2 In the tree, select Built-In>Air. 3 In the Add Material window, click Add to Component. MATERIALS ADD MATERIAL 1 Go to the Add Material window. 2 In the tree, select Built-In>Copper. 3 In the Add Material window, click Add to Component. 4 Close the Add Material window.
Square. 2 In the Square settings window, locate the Size section. 3 In the Side length edit field, type 0.1. 4 Locate the Position section. In the z edit field, type -0.05. Rectangle 1 1 In the Model Builder window, right-click Geometry 1 and choose Rectangle. 2 In the Rectangle settings window, locate the Size section. 3 In the Width edit field, type 0.08. 4 In the Height edit field, type 0.02. 5 Locate the Position section. In the z edit field, type -0.021. Circle 1 1 Right-click Geometry 1 and choose Circle. 2 In the Circle settings window, locate the Size and Shape section. 3 In the Radius edit field, type 0.0025. 4 Locate the Position section. In the r edit field, type 0.0125. 5 In the z edit field, type 0.0025. Circle 2 1 Right-click Geometry 1 and choose Circle. 2 In the Circle settings window, locate the Size and Shape section. 3 In the Radius edit field, type 0.0025. 4 Locate the Position section. In the r edit field, type 0.0185. 5 In the z edit field, type 0.0025.

I._M._Pei_and_his_most_iconic_buildings_建筑大师贝聿铭

最美的建筑，应该是建筑在时间之上的，时间会给出一切答案。

——贝聿铭I.M.Pei and his most iconic buildings建筑大师贝聿铭安徽王涛涛1Born in China,I.M.Pei (1917—2019)grew up in Suzhouand Shanghai before deciding to move to the United States to studyarchitecture.Pei was praised for giving “this century some of itsmost beautiful interior (内部的)spaces and exterior forms ”,said the jury of the Pritzker Architecture Prize,which he received in 1983.Below are four of his most iconic buildings.●Le Grande Louvre2In 1981,the newly elected French president,François Mitterrand,launched a cam⁃paign to renovate cultural institutions throughout France.One of the most advantageous ofthose projects was the renovation and remodeling of the Louvre.In 1983,after touring Eu⁃rope and the United States,President Mitterrand commissioned Chinese ⁃American archi⁃tect I.M.Pei.It was the first time that a foreign architect had been enlisted to work in Le Grande Louvre.●Bank of China Tower3When commissioned to design the Bank of China Tower on an intricate inland site,I.M.Pei was requested to create an unavoidably tall unique headquarters in a typhoon ⁃prone region that would represent the aspirations of the Chinese people.The solution as⁃similates architecture and engineering simultaneously,involving an asymmetrical tower that stands against both the skyline and the street.●Suzhou Museum4Founded in 1960and originally located in the Zhongwang Mansion of theTaipingHeavenly Kingdom(太平天国),Suzhou Museum has been a highly⁃regarded museum with a number of significant Chinese cultural relics.The new Suzhou Museum designed by I.M. Pei was completed in October2006.Not only does the museum become a monumental （意义深远的）design building in Suzhou,but also a significant construction,merging the traditional southern Chinese architecture style and modern aesthetics.●JFK Presidential Library5In1963,then President John F.Kennedy viewed possible sites for a presidential li⁃brary and museum to be built in his name.After several years,the John F.Kennedy Presi⁃dential Library was finally finished and dedicated on October20,1979.Architect I.M.Pei s signature geometric shapes of concrete steel and glass created an appropriate stately monu⁃mentality.A juxtaposition（并置）of spaces and light quality along with a defined and clear circulation（循环）creates a logical story⁃line of its namesake.ReadingCheckⅠ.Choose the best answers according to the textDetail 1.What can we learn about I.M.Pei from the text?A.He was born in Suzhou on May26,1917.B.He studied architecture both at home and abroad.C.He won the Pritzker Architecture Prize for Le Grande Louvre.D.He preferred concrete steel and glass in his design. Detail 2.Which building requires to show the willingness of the Chinese people?A.Le Grande Louvre.B.Bank of China Tower.C.Suzhou Museum.D.JFK Presidential Library. Detail 3.Which building best suits people who enjoy both traditional and mod⁃ern Chinese aesthetics?A.Le Grande Louvre.B.Bank of China Tower.C.Suzhou Museum.D.JFK Presidential Library. Inference 4.In which column is this text likely to appear?A.Adventures.B.Celebrities.C.Current affairs.D.Historic events.Ⅱ.DiscussionDo you agree with the author s attitude towards cultural confidence?And how to estab⁃lish your own cultural confidence?LanguageStudyComplete the following phrases according to the text 1.充满be of2.工业区park3.拆毁down 4.阐明light on 5.文化自信cultural 6.世界各地allthe worldⅡ.DiscussionWhat other great famous Chinese architects and their designs do you know?Pleasesearch for more information about them and share it with your classmates.Language StudyⅠ.Discover the useful structure in the textnot only...but (also)...意为“不仅……而且……”，用来连接两个表示并列关系的成分，also 可以省略。

What to do with disorder

Entropy rules!DisorderSqueezeCCCW 2011•What is disorder•Warning signs of disorder•Constraints and restraints in SHELXL •Using restraints to refine disorder•How to find the positions of disordered atoms•Disorder or no disorder?DisorderA disorder is a violation of the crystal symmetry and translation. The content of the asymmetric units is not identical, but it is identical on average .The obtained structure is an overlay, an average of all asymmetric units. Types of disorder:1.Substitutional disorderA crystallographic position is occupied by morethan one type of atom. This situation might occuroften in :•Compounds obtained by ion exchange •Minerals or ionic crystals (f. e. in zeolithes Si and Al share the same position)•Macromolecular compounds: Often water andsodium are found on the same position.•The disordered atoms might be found exactly on the same position or slightly displacedfrom each other.FeBr Br N N Fe Cl Br Types of disordertBu2.Positional disorderAn atom might be found in more than one position.Typical examples are:•Rotational disorder: A group with rotational freedom might be found in two differentrotatmers. A typical example is the tert -butylgroup.•Pseudorotational disorder:Saturated cycles might also be found in two conformations next to each other. THF is a typical example.OM•Whole molecule disorder:Most often found for co-crystallised solvents, especially if they are found around a symmetry element. The disorder assures that the crystal symmetry is kept in average, even if the solvent molecule itself does not contain this symmetry. Whole molecule disorder of the complete structure is a controversial subject and might often be a result of another effect (twinning, wrong space group etc.)Non-centrosymmetric 50%+ 50%=Non-centrosymmetric Inversion centerTypes of disorderStatic disorder: Atoms do not change their position during data collection (substitutional disorders are (normally) static disorders).Dynamic disorder:During data collection the atoms migrate between their respective positions.Static and dynamic disorders are treated identically during refinement.Strong thermal motion:Due to the limitations of the model, strong thermal motion is sometimes better treated as disorder.Warning signs of disorder:1.Substitutional disorder• a thermal factor too big or too small,•orientation of the ellipsoid parallel to abond, and/or•an incorrect bond distance•CHECKCIF: Hirshfeld test violation MBr Cl MHirshfeld rigid-bond testAnthony L. Spek (author of PLATON), Acta Cryst. (2009). D65, 148–155“The Hirshfeld rigid-bond test (Hirshfeld, 1976) has proved to be very effective in revealing problems in a structure. It is assumed in this test that two bonded atoms vibrate along the bond with approximately equal amplitude. Significant differences, i.e. those which deviate by more than a few standard uncertainties from zero, need closeexamination.Notorious exceptions are metal-to-carbonyl bonds, which generally show much larger differences (Braga & Koetzle, 1988).”Hirshfeld, F. L. (1976). Acta Cryst. A32, 239–244.Braga, D. & Koetzle, T. F. (1988). Acta Cryst. B44, 151–156.Warning signs of disorder2. Pseudorotational disorder•Increase(compared to neighbours)thermic ellipsoids•Shortened C-C distances•Flattened saturated carbocyclesd CC=1.42 Å3. Rotational disorder•Increased thermal ellipsoids•Electron density present between therefined atom positionsWarning signs of disorder4. Whole molecule disorder of solvent•Symmetric distribution of electron density around a symmetry elementTreating disorderAdditional sources:•Peter Müller, Crystal Structure Refinement: A Crystallographer’s Guide to SHELXLOxford University Press 2006.•Peter Müller’s small disorder tutorial:http://shelx.uni-ac.gwdg.de/~peterm/tutorial/disord.htmA disorder is a distribution of an atom over several positions or the sharing of a position by several atoms. In both cases, we are dealing with overlapping atoms of reduced electron density. Disorder refinement is thus always done using restraints.We want to use the smallest number and weakest restraints possible, but do not hesitate to use them in big numbers to avoid obtaining dubious results.Constraints and restraintsConstraint:Exact mathematical condition, which results in a reduction of the number of parameters. A constraint cannot be violated. Example: rigid groups and “riding”hydrogen atoms.Restraint:Additional observations/restraints which are added to the data during refinement. Restraints can be violated to a certain degree.M= Σw x(F o2 –F c2)2+ Σw r(T target–T c)2Both, constraints and restraints increase the data/parameterratio.•Special positions (generated automatically)These constraints, which are necessary for atoms positioned on symmetry elements, are automatically generated by the program.Types of constraints used in the SHELX programpackagecorrect wrong wrongcorrectFile *.lst:Special position constraints for Zr1x = 0.0000 z = 0.2500 U23 = 0 U12 = 0 sof = 0.50000AFIX 66C1 x y z :C6 x y z AFIX 0AFIX 56C1 x y z :C5 x y z AFIX 0AFIX 106C1 x y z :C10 x y z AFIX 0AFIX 116C1 x y z:C11 x y zAFIX 0•Special positions (generated automatically)•Rigid groups (e. g. AFIX x6 …AFIX 0)In rigid groups the parameters for all atomic positions (3 x n) are replaced by 3 rotations and 3 translations for the complete group. The idealized geometry of the group is fixed and the atoms cannot move independently. AFIX x 6: completely rigid group; AFIX x 9: group can grow and shrink keeping its relative geometry.Types of constraints used in the SHELX programpackage•Special positions (generated automatically)•Rigid groups (e. g. AFIX x6 …AFIX 0)•“Riding model”for hydrogen atoms (AFIX mn)x H = x C +Δxy H = y C + Δyz H = z C +ΔzU H = 1.2 ·U XNo additional parameters are refined for the hydrogen atoms, if they are treated by a riding model!Types of constraints used in the SHELX programpackageXHH H•Special positions (generated automatically)•Rigid groups (e. g. AFIX x6 …AFIX 0)•“Riding model”for hydrogen atoms (AFIX mn)•Fixed parametersAddition of 10 excludes a value from the refinement. Normally occupation factors are not refined.(The program adds automatically the constraints for atoms on special positions.)Types of constraints used in the SHELX programpackageC1 1 0.31357 0.46194 0.73087 11.000000.03221 0.02339 =0.02334 0.00728 0.00820 0.00568C2 1 0.17696 0.500000.65307 10.500000.03174 0.02909 =0.02961 0.01051 0.00909 0.00550C3 1 0.13022 0.26106 0.57225 11.000000.03871 0.02965 =0.03073 0.00631 0.00674 -0.00625d cdσ= 0.1σ= 0.5In contrast to constraints, which cannotbe violated, restraints define only a target value for some parameters. They are associated with a standard deviationσ, which describes how much aviolation of the target value is penalised.The smaller σ, the more the parameteris forced to be close to the targetedvalue d c . A σ= 0 yields a constraint.M = Σw x (F o 2–F c 2)2+ Σ1/σ(d –d c )2Restraints in SHELXDFIX, DANG, SADI, SAME:distances and angles (1,3-distances)DELU, SIMU, ISOR:thermal motion parametersFLAT, CHIV, BUMP, NCSY, SUMPRestraints Free variablesIn SHELXL, each value is provided in the form of x = 10m + p .p : value, which is refined; m : refinement modem = 0: normal refinement, x = pm = 1: no refinement, x is fixed at p C1 1 0.31357 0.46194 0.73087 11.00000 0.03221 C2 1 0.17696 0.39844 0.65307 11.00000 10.035C3 1 0.13022 0.26106 0.57225 11.00000 10.035CL1 2 0.25000 0.17682 0.50000 10.50000 0.05684 Br1 3 0.25000 0.19763 0.50000 10.50000 0.05110C1 1 0.31357 0.46194 0.73087 11.00000 0.03221 C2 1 0.17696 0.39844 0.65307 11.00000 10.035C3 1 0.13022 0.26106 0.57225 11.00000 10.035CL1 2 10.250000.17682 10.5000010.50000 0.05684 Br1 3 10.250000.19763 10.5000010.50000 0.05110Values fixed at 1.0000Values fixed at 0.035Values fixed at 0.5000•We can exclude any value from refinement by adding 10.•For atoms on special positions, the program does this automatically without our intervention.Free variablesIn SHELXL, each value is provided in the form of x= 10m+ p.p: value, which is refined; m: refinement modem= 0: normal refinement, x= pm= 1: no refinement, x is fixed at pm> 1: x= p ·”free variable no. m”m<-1: x= p ·(1 -”free variable no. m”)The same value is refined for all three atoms FVAR 0.73503 0.0239 0.2365C1 1 0.31357 0.46194 0.73087 11.00000 21.00000C2 1 0.17696 0.39844 0.65307 11.00000 21.00000C3 1 0.13022 0.26106 0.57225 11.00000 21.00000CL1 2 0.25000 0.17682 0.50000 31.00000 0.05684Br1 3 0.25000 0.19763 0.50000 -31.00000 0.05110Using the m<-1 option, a ratio can be defined with a fixed sum of the two variables: 31.000 + -31.0000 = 1(10m)p + (-10m)p = p30.500 + -30.5000 = 0.5Free variable no. m, targetvalue pFree variablesIn SHELXL, each value is provided in the form of x= 10m+ p.p: value, which is refined; m: refinement modem= 0: normal refinement, x= pm= 1: no refinement, x is fixed at pm> 1: x= p·”free variable no. m”m<-1: x= p·(1 -”free variable no. m”)FVAR 0.735030.0239 0.2365•There is no “free variable no. 1”, since adding 10 is used to exclude values from refinement.•The first position of the FVAR command is thus occupied by the “overall scale factor”(OSF).•The OSF scales our (arbitrary) intensities, which depends on crystal size, detector sensitivity etc., to the theoretical diffraction by a single unit cell.Free variables In SHELXL, each value is provided in the form of x = 10m + p .p : value, which is refined; m : refinement modem = 0: normal refinement, x = pm = 1: no refinement, x is fixed at pm > 1: x = p ·”free variable no. m ”m <-1: x = p ·(1 -”free variable no. m ”)FVAR 0.73503 0.64390.2365C1 1 0.31357 0.46194 0.73087 11.00000 0.03221 C2 1 0.17696 0.39844 0.65307 21.00000 10.035C3 1 0.13022 0.26106 0.57225 -21.00000 10.035CL1 2 0.250000.17682 0.5000030.50000 0.05684 Br1 3 0.250000.19763 0.50000-30.50000 0.05110 Value fixed at 1.0000Value fixed at 0.035Value fixed at: 1.0000 x var. #2 = 0.6439Value fixed at: 1.0000 x (1-var. #2) = 0.2561Value fixed at: 0.50000 x var. #3 = 0.1183Value fixed at: 0.50000 x (1-var. #3) = 0.3817Constraints for special positions are automatically generated by the program.How to use restraints to refine disorder1.Position restraintsRestraints are never directly on a position, but always on interatomic distances and thus molecule geometry.SHELX does not offer angle restraints. Restraints on angles have thus to be effected by restraining the 1,3-distances of the atoms.DFIX d sd <atome 1> <atome 2> <atome 3> <atome 4> …Fixation of an interatomic distance between a pair (or pairs) of atoms to a specific value d with a standard deviation sd (default, if omitted).I discourage the excessive use of DFIX restraints, since they impose a bias/preconception on the structure. There are, however, occasions where the use of DFIX restraints is appropriate.Restraints in SHELXLO M SADI sd <atome 1> <atome 2> <atome 3> <atome 4> …Interatomic distances between pairs of atoms are restraint (with standard deviation sd , which can be omitted) to be equal. The actual value of these distances is free to refine.SADI is the most useful restraint for refining disorders. Without inflicting a preconception on the value of a distance, we can safely use our chemical/crystallographic knowledge to decide that two or more bonds should have identical values (in the margin of error of the provided standard deviation).The SAME command allows us to generate a multitude of SADI instructions with a single line.SADI C29 C30A C29 C30B C32 C31A C32 C31BSADI C30A C31A C30B C31BSADI O4 C30A O4 C30B O4 C31A O4 C31BSADI C32 C30A C32 C30B C29 C31A C29 C31BOMSAME commandSAME O4 C29 C30B C31B C32SAME O4 C32 C31B C30B C29O4 3 0.30266 -0.00504 -0.11751 [...]C29 1 0.19024 -0.06291 -0.13854 [...]C30A 1 0.12758 -0.13129 -0.06586 [...]C31A 1 0.27046 -0.15492 -0.01832 [...]C32 1 0.34071 -0.05601 -0.04205 [...]OMSADI C29 C30A C29 C30BSADI C32 C31A C32 C31BSADI C30A C31A C30B C31B SADI O4 C30A O4 C30B SADI O4 C31A O4 C31BSADI C32 C30A C32 C30BSADI C29 C31A C29 C31BSADI C29 C30A C29 C30B C32 C31A C32 C31B SADI C30A C31A C30B C31B SADI O4 C30A O4 C30B O4 C31A O4 C31BSADI C32 C30A C32 C30B C29 C31A C29 C31BOMIt is very important to have the atoms in the required order!Typographic errors here are fatal!SADI …continuedO M SADI C29 C30A C29 C30B C32 C31A C32 C31B =C30A C31A C30B C31B SADI O4 C30A O4 C30B O4 C31A O4 C31B = C32 C30A C32 C30B C29 C31A C29 C31BOM2. Thermal factor restraintsSIMU sd1 sd2 dmax[1.7] <atomlist, all atoms if omitted>Superimposed atoms share their electron density. There is thus a linear dependence between their thermic factors and their occupation factor. In cases of disorder, a command SIMU 0.04 0.080.9has to be always present . It ensures that superimposed atoms (distance < 0.8 Å) have identical thermal parameters and enables the refinement of their occupation.SIMUThis starts to violate chemical knowledge aboutequivalent bond and should only be done exceptionally.SIMU and DELUAnisotropic refinement : SIMU restraints for superimposed atoms can be accompanied by restraints DELU and/or SIMU for neighbouring atoms .SIMU C29 C30A C30B C31A C31B C32DELU C30A C31ADELU C30B C31BSIMU (without further values specified) uses a default distance of 1.7 Å, below which restraints are applied. In contrast to SIMU 0.04 0.08 0.9,we thus have to specify the atoms to which we apply the restraint. Otherwise it is applied to the whole structure.SIMU : Equivalence of all thermal factorsDELU : Equivalence of the thermal factors parallel to a bond (c. f. Hirshfeld test )SIMUDELUEADP and ISOREADP <atoms>•The same anisotropic parameters are used for all atoms •Useful, par ex. for opposite fluorines in PF 6-or disordered CF 3EADP is a powerful constraint but should be used onlyexceptionally. There is in most cases no good reason why two independent atoms should have the same anisotropic parameters. ISOR•Forces the anisotropic parameters to become more isotropic•Last resort for non-positive defined atomsF 1P F 6F 4F 3F 5F 2EADP F1 F6Non-positive defined: An atom is called “non-positive defined”, if at least one of its radii refined to an negative value (which of course does not make any physical sense). Non-positive defined atoms indicate severe problems, very often wrong atom assignments or low data-parameter ratios. These problems have to be addressed!Use of an ISOR restraint is acceptable as a last resort only , when we can define the source of the problem and its not a structural one, other measures were unsuccessful (i. e. SIMU restraints) and we comment on this clearly in the manuscript text and the CIF.Example for using restraintsF 1P F 6F 4F 3F5F 2SADI P1 F1 P1 F2 P1 F3 P1 F4 P1 F5 P1 F6SADI F1 F2 F1 F3 F1 F4 F1 F5 F2 F3 F2 F6 =F2 F5 F3 F6 F3 F4 F5 F6SADI F1 F6 F2 F4 F3 F5EADP F1 F6EADP F2 F4EADP F3 F5P1 4 0.424356 -0.021611 0.009848 10.50000 0.06381 0.03516 […]F1 5 0.327987 0.417746 0.265512 11.00000 0.06119 0.06335 […]F2 5 0.385421 0.357821 0.166673 11.00000 0.05997 0.06456 […]F3 5 0.265277 0.346163 0.220067 11.00000 0.06713 0.07757 […]F4 5 0.519635 0.310843 -0.088822 11.00000 0.06978 0.07860 […]F5 5 0.545683 0.299782 0.052783 11.00000 0.05744 0.07086 […]F6 5 0.587478 0.232770 0.100987 11.00000 0.06598 0.07993 […]Example PF 6-: Due to their nearly spherical nature PF 6anions are often found disordered or at least showing high thermal parameters indicating not well localized atoms. In these cases refinement with restraints is often necessary, when the geometry of the anions becomes unreasonable. (I. e. variations of more than 10% in P-F bond lengths.)Often several SADI commands might be replaced by oneSAME commandPARTPART n•Not a restraint•No influence on the refinement•Influence on the connectivity list•n > 1: Atoms with this part number can be bonded to all other atoms with PART number n and all atoms with n=0.•n < 0: Atoms can be bonded to all atoms with PART 0 and PART n, but not to those generated by a symmetry operation.•Avoids unnecessary bonds in molecular drawings•essential if AFIX is used for hydrogen atoms in disordered groups PART 0PART 1PART 2PART 1PART -1Occupation factor PART -1C20 1 0.424356 -0.021611 0.009848 10.50000 0.06381 0.03516 =0.05315 -0.00588 0.00671 -0.00304C21 1 0.428540 0.011059 -0.068300 10.50000 0.06186 0.05445 =0.03609 0.00542 -0.01401 0.00890[...]C24 1 0.634868 0.025612 0.045748 10.50000 0.04323 0.05896 =0.04699 -0.00149 -0.01253 0.00164C25 1 0.530284 -0.013916 0.066481 10.500000.05856 0.06452 =0.04128 -0.01875 -0.02223 0.02545C26 1 0.312605 -0.062961 0.030505 10.50000 0.09882 0.09599 =0.07637 -0.00566 0.01279 -0.06335PART 0Disordered toluenePART 1PART -1Thermalparameters needattention!Occupation factorFVAR 0.42837 0.58208[...]O4 3 0.302705 -0.005024 -0.117529 11.00000 0.03588 0.04172 =0.02975 -0.00291 -0.00309 -0.01165C29 1 0.190224 -0.062926 -0.138556 11.00000 0.04345 0.05179 =0.05469 -0.01254 -0.00430 -0.02030PART 1C30A 1 0.127840 -0.130979 -0.065373 21.000000.05283 0.06736 =0.07186 0.00717 0.00151 -0.02926C31A 1 0.274211 -0.156883 -0.019306 21.000000.05632 0.05613 =0.05575 -0.00802 -0.00165 -0.01273PART 2C30B 1 0.191961 -0.163582 -0.084484 -21.000000.05715 0.05259 =0.07274 -0.01448 0.01353 -0.02752C31B 1 0.208671 -0.126727 -0.015288 -21.000000.05579PART 0C32 1 0.340691 -0.056023 -0.042066 11.00000 0.07080 0.06487 =0.02841 0.00483 -0.00617 -0.02682Disordered THF= 1.000* FVAR #2 = 0.58208= 1-1.000* FVAR #2 = 0.41792PART 1PART 2How to find the positions of disordered atoms?*.lst:Principal mean square atomic displacements U[…]0.3098 0.0893 0.0464 C4 may be split into 0.6218 0.2673 0.2408and 0.6118 0.2471 0.26660.3100 0.0924 0.0392 C5 may be split into 0.5976 0.3191 0.3424and 0.5834 0.3017 0.3597*.res:C4 1 0.620102 0.244385 0.267042 11.00000 0.03885 0.06703 =0.03096 0.00488 -0.00631 -0.00106C5 1 0.592263 0.310218 0.343259 11.00000 0.03679 0.05091 =0.04370 0.01162 -0.00769 0.00426*.ins:FVAR 0.293 0.4[…]PART 1C4A 1 0.6218 0.2673 0.240821.000000.04C5A 1 0.5834 0.3017 0.3597 21.000000.04PART 2C4B 1 0.6118 0.2471 0.2666 -21.000000.04C5B 1 0.5976 0.3191 0.3424 -21.000000.04PART 01. Warnings in the output file .lst2. Inforce the refinement starting from the original positions using restraints C2C3A C3BC4C1C1 1 0.519760 0.310792 -0.089059 11.00000 0.06836C2 1 0.545505 0.299615 0.052950 11.00000 0.05727 C3A 1 0.587307 0.232816 0.100964 11.00000 0.06729 C4 1 0.621837 0.265112 0.234704 11.00000 0.08464C3B 1 0.563423 0.245364 0.134634 11.00000 0.07693C5 1 0.582099 0.301674 0.361645 11.00000 0.08794SADI C1 C2A C1 C3A C1 C4A C1 C2B C1 C3B C1 C4BSADI C2A C3A C3A C4A C4A C2A C2B C3B C3B C4B C4B C2BFVAR 0.2340.6[…]C1 1 0.519760 0.310792 -0.089059 11.00000 0.06836PART 1C2A 1 0.545505 0.299615 0.05295021.00000 0.05727C3A 1 0.587307 0.232816 0.100964 21.000000.06729C4A 1 0.621837 0.265112 0.23470421.00000 0.08464PART 2C2B 1 0.545505 0.299615 0.052950-21.000000.05727C3B 1 0.563423 0.245364 0.134634 -21.000000.07693C4B 1 0.621837 0.265112 0.234704-21.000000.08464PART 0C5 1 0.582099 0.301674 0.361645 11.00000 0.08794How to find the positions of disorderd atoms? 3. Using rigid groups (AFIX)C1C2C3C4C5C6FVAR 0.234 0.4[…]PART 1 21.0000AFIX 66C1A 1 0.519760 0.310792 -0.089059 11.00000 0.06836C2A 1 0.545505 0.299615 0.052950 11.00000 0.05727 C3A 1 0.587307 0.232816 0.100964 11.00000 0.06729C4A 1 0.621837 0.265112 0.234704 11.00000 0.08464C5A 1 0.587307 0.232816 0.100964 11.00000 0.06729 C6A 1 0.582099 0.301674 0.361645 11.00000 0.08794AFIX 0PART 2 -21.0000AFIX 66C1B 1 0.519760 0.310792 -0.089059 11.00000 0.06836 C2B 1 0.545505 0.299615 0.052950 11.00000 0.05727C3B 1 0.587307 0.232816 0.100964 11.00000 0.06729C4B 1 0.621837 0.265112 0.234704 11.00000 0.08464C5B 1 0.587307 0.232816 0.100964 11.00000 0.06729C6B 1 0.582099 0.301674 0.361645 11.00000 0.08794AFIX 0PART 0C1C2C3C4C5C6All occupation factors are replaced bythe second value of the PART command.Copy/paste: Identical start positions How to find the positions of disorderd atoms?4. Using rigid groups II FVAR 0.234 0.4[…]PART 1 21.0000AFIX 66C3A 1 0.6433 0.2938 0.110911.00000 0.06836 C4A 1 0.6218 0.2673 0.240811.00000 0.05727 C5A 1 0.5976 0.3191 0.342411.00000 0.06729 C6A 1 0 0 0 11.00000 0.05C1A 1 0 0 0 11.00000 0.05C2A 1 0 0 0 11.00000 0.05AFIX 0PART 2 -21.0000AFIX 66C3B 1 0.6322 0.2673 0.132011.00000 0.06836 C4B 1 0.6118 0.2471 0.266611.000000.05727 C5B 1 0.5976 0.3191 0.342411.00000 0.06729 C6B 1 0 0 0 11.00000 0.05C1B 1 0 0 0 11.00000 0.05C2B 1 0 0 0 11.00000 0.05AFIX 0PART 0C1C2C3C4C5C6*.lst:Principal mean square atomic displacements U[…]0.2998 0.0292 0.0374 C3 may be split into 0.6433 0.2938 0.1109and 0.6322 0.2673 0.13200.3098 0.0893 0.0464 C4 may be split into 0.6218 0.2673 0.2408and 0.6118 0.2471 0.2666With the three first positionsdefined, AFIX 66 can complete thecycle automatically.How to find the positions of disorderd atoms?Stepwise refinement of disorder*.lst:Principal mean square atomic displacements U[…]0.3098 0.0893 0.0464 C4 may be split into 0.6218 0.2673 0.2408and 0.6118 0.2471 0.26660.3100 0.0924 0.0392 C5 may be split into 0.5976 0.3191 0.3424and 0.5834 0.3017 0.3597*.ins:SADI C2 C4A C2 C4B C6 C5A C6 C5BSADI C4A C4B C5A C5BSADI C2 C5A C2 C5B C6 C4A C6 C4B[…]PART 1C4A 1 0.6218 0.2673 0.240810.5000010.03C5A 1 0.5834 0.3017 0.3597 10.5000010.03PART 2C4B 1 0.6118 0.2471 0.2666 10.50000 10.03C5B 1 0.5976 0.3191 0.3424 10.50000 10.03PART 01. Assigning initial positionsCheck if atoms are assigned correctedly. If necessary switchatoms around.Stepwise refinement of disorder PART 1C4A 1 0.6218 0.2673 0.240810.5000010.03C5A 1 0.5834 0.3017 0.3597 10.5000010.03PART 2C4B 1 0.6118 0.2471 0.2666 10.50000 10.03C5B 1 0.5976 0.3191 0.3424 10.50000 10.03PART 02. Refining the occupation factorFVAR 0.293 0.4[…]PART 1C4A 1 0.6218 0.2673 0.2408 21.0000010.03C5A 1 0.5834 0.3017 0.3597 21.0000010.03PART 2C4B 1 0.6118 0.2471 0.2666 -21.0000010.03C5B 1 0.5976 0.3191 0.3424 -21.0000010.03Stepwise refinement of disorder FVAR 0.293 0.4[…]PART 1C4A 1 0.6218 0.2673 0.2408 21.0000010.03C5A 1 0.5834 0.3017 0.3597 21.0000010.03PART 2C4B 1 0.6118 0.2471 0.2666 -21.0000010.03C5B 1 0.5976 0.3191 0.3424 -21.0000010.03 3. Freeing isotropic refinementSIMU 0.02 0.04 0.8FVAR 0.293 0.265[…]PART 1C4A 1 0.6218 0.2673 0.2408 21.00000 0.03C5A 1 0.5834 0.3017 0.3597 21.00000 0.03PART 2C4B 1 0.6118 0.2471 0.2666 -21.00000 0.03C5B 1 0.5976 0.3191 0.3424 -21.00000 0.03PART 0Stepwise refinement of disorder[…]PART 1C4A 1 0.6218 0.2673 0.2408 21.00000 0.04213C5A 1 0.5834 0.3017 0.3597 21.00000 0.03812PART 2C4B 1 0.6118 0.2471 0.2666 -21.00000 0.03932C5B 1 0.5976 0.3191 0.3424 -21.00000 0.04098PART 04. Anisotropic refinement[…]ANIS C4A C4B C5A C5BPART 1C4A 1 0.6218 0.2673 0.2408 21.00000 0.04213C5A 1 0.5834 0.3017 0.3597 21.00000 0.03812PART 2C4B 1 0.6118 0.2471 0.2666 -21.00000 0.03932C5B 1 0.5976 0.3191 0.3424 -21.00000 0.04098PART 0Stepwise refinement of disorder[…]PART 1C4A 1 0.6218 0.2673 0.2408 21.00000 0.03221 0.02339 =0.02334 0.00728 0.00820 0.00568C5A 1 0.5834 0.3017 0.3597 21.00000 0.03174 0.02909 =0.02961 0.01051 0.00909 0.00550PART 2C4B 1 0.6118 0.2471 0.2666 -21.00000 0.03871 0.02965 =0.03073 0.00631 0.00674 -0.00625C5B 1 0.5976 0.3191 0.3424 -21.00000 0.03221 0.02339 =0.02334 0.00728 0.00820 0.00568PART 05. Check the results!•Check bond lengths-> decrease sigma for restraints if necessary •Check thermal parameters-> decrease sigma for SIMU, introduceaddtional SIMU with a distance of 1.6, introduce DELU. If necessary, return to isotropicDisorder solving strategy1.Identify the disorder (does it make sense ?)2.Find the positions3.Refine with the necessary constraints and restraints4.Refine anisotropic5.Apply restraints/constraints for the anisotropicrefinement if necessary. (SIMU 0.02 0.04 0.8 is always present!)6.Decide to return to isotropic refinement or not7.(Try to lighten or delete restraints/constraints)8.Arrive at a solution which contains the least number of restraints/constraints, but is in reasonable agreement with “reality”.Twinnig and disorderA disorder, which is not a disorder but hidden order :•Twinning•SuperstructuresSome twinned crystals might simulate the presence of a symmetry element and a higher space group symmetry of a disordered structure.Disorder?+A A +A ++A A +A ++A +A A ++A +A +A +A A +A +A +A +A +A +A +A +A +A +A +A +A +A +A +A +A ++A +A +A +A +A +A +A +A +A +A +A +A +A +A +A Twinning !+A +Superstructures and disorderA disorder, which is not a disorder but hidden order :•Twinning•SuperstructuresSuperstructure: A disorder which is not random, but follows a certain order with a periodicity which is bigger than that of the unit cell.A +A +A +A +A +A +A +A +A ++A +A +A +A+A +A A +A ++A +A A +A ++A +A A +A ++A +++Disorder?A ++A +AA +Superstructure!An examplea *a *mailledoubléeAn examplea*a*double sizedunit cell Fin。

usp32 616 BULK DENSITY AND TAPPED DENSITY 堆密度和振实密度 ——中英对照

616BULK DENSITY AND TAPPED DENSITY松密度和紧密度The bulk density of a solid is often very difficult to measure since the slightest disturbance of the bed may result in a new bulk density. Moreover, it is clear that the bulking properties of a powder are dependent on the “history” of the powder (e.g., how it was handled), and that it can be packed to have a range of bulk densities. Thus, it is essential in reporting bulk density to specify how the determination was made.固体的松密度的测量很困难，测量时，轻微的震动就会导致松密度的不同。

因此，可以知道粉末的松散性取决于粉末的来历。

而且压紧之后，会有一个密度范围。

因此，报告松密度时，必须说明结果是如何得到的。

Because the interparticulate interactions that influence the bulking properties of a powder are also the interactions that interfere with powder flow, a comparison of the bulk and tapped densities can give a measure of the relative importance of these interactions in a given powder. Such a comparison is often used as an index of the ability of the powder to flow. The bulk density often is the bulk density of the powder “as poured” or as passively filled into a measuring vessel. The tapped density is a limiting density attained after “tapping down,” usually in a device that lifts and drops a volumetric measuring cylinder containing the powder a fixed distance.微粒的相互作用不仅影响粉末的松散性，而且影响粉末的流速。

cif详解

data_NJU_audit_creation_method SHELXL-97 产生CIF的程序名称_chemical_name_systematic 化合物的系统命名;?;_chemical_name_common ? 化合物的俗名_chemical_melting_point ? 化合物的熔点_chemical_formula_moiety'C15 H13 N3 O' 化合物的化学式_chemical_formula_sum'C15 H13 N3 O'_chemical_formula_weight 251.28 化合物的化学式量loop__atom_type_symbol 构成化合物的原子散射因子来源_atom_type_description_atom_type_scat_dispersion_real_atom_type_scat_dispersion_imag_atom_type_scat_source'C' 'C' 0.0033 0.0000'International Tables Vol C Tables 4.2.6.8 and 6.1.1.4''H' 'H' 0.0000 0.0000'International Tables Vol C Tables 4.2.6.8 and 6.1.1.4''N' 'N' 0.0061 0.0000'International Tables Vol C Tables 4.2.6.8 and 6.1.1.4''O' 'O' 0.0106 0.0000'International Tables Vol C Tables 4.2.6.8 and 6.1.1.4'_symmetry_cell_setting 'Triclinic' 晶系名称_symmetry_space_group_name_H-M 'Pc ' 空间群名称loop__symmetry_equiv_pos_as_xyz'x, y, z''x, -y, z+1/2' 晶胞中等效坐标_cell_length_a 12.608(8) 晶胞参数_cell_length_b 11.023(7)_cell_length_c 10.044(7)_cell_angle_alpha 90.00_cell_angle_beta 105.94(3)_cell_volume 1342.2(15)_cell_formula_units_Z 4_cell_measurement_temperature 291(2) 测量晶胞时的温度_cell_measurement_reflns_used 940 用于确定晶胞的衍射点数_cell_measurement_theta_min 2.50 用于确定晶胞的衍射点的最小θ值_cell_measurement_theta_max 20.48 用于确定晶胞的衍射点的最大θ值_exptl_crystal_description block 被测单晶的外观形状_exptl_crystal_colour colourless 被测单晶的外观颜色_exptl_crystal_size_max 0.30 被测单晶的外观尺寸_exptl_crystal_size_mid 0.26_exptl_crystal_size_min 0.24_exptl_crystal_density_meas ? 被测单晶的测量密度_exptl_crystal_density_diffrn 1.244 被测单晶的计算密度_exptl_crystal_density_method 'not measured' 测量单晶密度方法_exptl_crystal_F_000 528 单胞中电子数_exptl_absorpt_coefficient_mu 0.081 单胞的线性吸收系数_exptl_absorpt_correction_type 'multi-scan' 吸收校正方法）_exptl_absorpt_correction_T_min 0.98 最小透过率_exptl_absorpt_correction_T_max 0.98 最大透过率_exptl_absorpt_process_details 'SADABS; Bruker, 2000' 吸收校正所用方法及其文献_exptl_special_details;? （实验细节描述）;_diffrn_ambient_temperature 291(2) 衍射实验时温度_diffrn_radiation_wavelength 0.71073 衍射线波长λ_diffrn_radiation_type 'MoK\a' 衍射光源_diffrn_radiation_source 'sealed tube' X-光管类型_diffrn_radiation_monochromator 'graphite' 单色器类型_diffrn_measurement_device_type 'Bruker Smart Apex CCD area detector' 衍射仪型号_diffrn_measurement_method 'phi and omega scans' 收集衍射数据的方式_diffrn_detector_area_resol_mean ?_diffrn_standards_number ? 设置标准衍射点数_diffrn_standards_interval_count ? 标准衍射测量衍射点间隔_diffrn_standards_interval_time ? 标准衍射测量时间间隔_diffrn_standards_decay_% ? 测量过程中是否有衰减_diffrn_reflns_number 11645 总衍射点数_diffrn_reflns_av_R_equivalents 0.0437 等效点平均标准误差_diffrn_reflns_av_sigmaI/netI 0.0321 平均背景强度与平均衍射强度之比_diffrn_reflns_limit_h_min -16 衍射指标范围_diffrn_reflns_limit_k_min -13_diffrn_reflns_limit_k_max 14_diffrn_reflns_limit_l_min -13_diffrn_reflns_limit_l_max 12_diffrn_reflns_theta_min 1.68 结构精修时最小θ角_diffrn_reflns_theta_max 27.74 结构精修时最大θ角_reflns_number_total 3110 独立衍射点数_reflns_number_gt 2784 独立衍射点中强度大于2σ的衍射点数_reflns_threshold_expression >2sigma(I)_computing_data_collection 'SMART (Bruker, 2000)' 收集衍射数据所用程序_computing_cell_refinement 'SMART' 精修晶胞参数所用程序_computing_data_reduction 'SAINT (Bruker, 2000)' 衍射数据还原所用程序_computing_structure_solution 'SHELXTL (Bruker, 2000)' 解析粗结构所用程序_computing_structure_refinement 'SHELXTL' 结构精修所用程序_computing_molecular_graphics 'SHELXTL' 发表论文作图所用程序_computing_publication_material 'SHELXTL' 发表论文制作数据表格所用程序_refine_special_details 结构精修过程中一些细节的说明;Refinement of F^2^ against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F^2^, conventional R-factors R are basedon F, with F set to zero for negative F^2^. The threshold expression ofF^2^ > 2sigma(F^2^) is used only for calculating R-factors(gt) etc. and isnot relevant to the choice of reflections for refinement. R-factors basedon F^2^ are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.;_refine_ls_structure_factor_coef Fsqd 基于F2的结构精修_refine_ls_matrix_type full 精修矩阵类型_refine_ls_weighting_scheme calc 权重方案_refine_ls_weighting_details 权重方案表达式'calc w=1/[\s^2^(Fo^2^)+(0.05P)^2^+0.88P] where P=(Fo^2^+2Fc^2^)/3'_atom_sites_solution_primary direct 解析粗结构的方法_atom_sites_solution_secondary difmap 进一步解析结构的方法_atom_sites_solution_hydrogens geom 获得氢原子的方法_refine_ls_hydrogen_treatment mixed 结构精修中氢原子的处理方法_refine_ls_extinction_method none 消光校正方案_refine_ls_extinction_coef ? 消光校正系数_refine_ls_abs_structure_details 处理绝对构型方法和参考文献'Flack H D (1983), Acta Cryst. A39, 876-881'_refine_ls_abs_structure_Flack 10(10) 绝对构型参数_refine_ls_number_reflns 3110 参加结构精修的衍射点数_refine_ls_number_parameters 349 参加结构精修的参数数目_refine_ls_number_restraints 2 结构精修中几何限制数目_refine_ls_R_factor_all 0.0675 对全部衍射点的R1值_refine_ls_R_factor_gt 0.0593 对可观察衍射点的R1值_refine_ls_wR_factor_ref 0.1338 对全部衍射点的wR2值_refine_ls_wR_factor_gt 0.1302 对可观察衍射点的wR2值_refine_ls_goodness_of_fit_ref 1.012 对可观察衍射点的S值_refine_ls_restrained_S_all 1.011 对全部衍射点的S值_refine_ls_shift/su_max 0.000 最后精修过程的漂移值_refine_ls_shift/su_mean 0.000 最后精修过程的平均漂移值loop_ 结构中各原子坐标, 各向同性振动参数, 原子占有率等_atom_site_label_atom_site_type_symbol_atom_site_fract_x_atom_site_fract_y_atom_site_fract_z_atom_site_U_iso_or_equiv_atom_site_adp_type_atom_site_occupancy_atom_site_symmetry_multiplicity_atom_site_calc_flag_atom_site_refinement_flags_atom_site_disorder_assembly_atom_site_disorder_groupC1 C 1.2011(4) 0.4816(5) 0.8674(5) 0.0472(10) Uani 1 1 d . . .H1 H 1.2238 0.5562 0.8420 0.057 Uiso 1 1 calc R . .C2 C 1.2551(4) 0.4303(4) 0.9917(5) 0.0457(10) Uani 1 1 d . . .H2 H 1.3139 0.4716 1.0505 0.055 Uiso 1 1 calc R . .C3 C 1.2239(4) 0.3174(4) 1.0323(5) 0.0417(9) Uani 1 1 d . . .H3 H 1.2609 0.2838 1.1173 0.050 Uiso 1 1 calc R . .C4 C 1.1362(4) 0.2566(4) 0.9422(4) 0.0418(10) Uani 1 1 d . . .H4 H 1.1148 0.1809 0.9666 0.050 Uiso 1 1 calc R . .C5 C 1.0805(4) 0.3081(5) 0.8167(4) 0.0469(11) Uani 1 1 d . . .H5 H 1.0219 0.2672 0.7571 0.056 Uiso 1 1 calc R . .C6 C 1.1126(3) 0.4217(4) 0.7798(5) 0.0421(9) Uani 1 1 d . . .C7 C 1.0508(3) 0.4875(4) 0.6585(5) 0.0426(10) Uani 1 1 d . . .H7 H 1.0694 0.5672 0.6446 0.051 Uiso 1 1 calc R . .C8 C 0.9646(4) 0.4321(4) 0.5637(5) 0.0436(10) Uani 1 1 d . . .H8 H 0.9451 0.3521 0.5747 0.052 Uiso 1 1 calc R . .C9 C 0.9049(4) 0.5050(4) 0.4446(4) 0.0435(10) Uani 1 1 d . . .C10 C 0.6810(4) 0.4686(4) 0.1451(4) 0.0391(9) Uani 1 1 d . . . C11 C 0.5998(4) 0.5425(4) 0.0516(4) 0.0438(10) Uani 1 1 d . . . C12 C 0.5471(3) 0.5017(4) -0.0823(4) 0.0356(8) Uani 1 1 d . . . H12 H 0.5587 0.4233 -0.1093 0.043 Uiso 1 1 calc R . .C13 C 0.4793(4) 0.5778(4) -0.1716(5) 0.0413(9) Uani 1 1 d . . . H13 H 0.4438 0.5497 -0.2599 0.050 Uiso 1 1 calc R . .C14 C 0.5136(4) 0.7372(4) -0.0082(4) 0.0427(9) Uani 1 1 d . . . H14 H 0.5025 0.8165 0.0165 0.051 Uiso 1 1 calc R . .C15 C 0.5845(3) 0.6620(4) 0.0872(4) 0.0432(10) Uani 1 1 d . . . H15 H 0.6216 0.6914 0.1743 0.052 Uiso 1 1 calc R . .C16 C 0.4052(4) 0.0511(4) -0.2985(4) 0.0424(9) Uani 1 1 d . . . H16 H 0.4482 -0.0181 -0.2728 0.051 Uiso 1 1 calc R . .C17 C 0.3238(3) 0.0544(4) -0.4232(4) 0.0400(9) Uani 1 1 d . . . H17 H 0.3127 -0.0128 -0.4814 0.048 Uiso 1 1 calc R . .C18 C 0.2588(4) 0.1560(4) -0.4623(5) 0.0455(10) Uani 1 1 d . . . H18 H 0.2039 0.1569 -0.5459 0.055 Uiso 1 1 calc R . .C19 C 0.2761(4) 0.2580(4) -0.3752(4) 0.0417(9) Uani 1 1 d . . . H19 H 0.2328 0.3269 -0.4015 0.050 Uiso 1 1 calc R . .C20 C 0.3577(3) 0.2565(4) -0.2498(4) 0.0356(8) Uani 1 1 d . . . H20 H 0.3689 0.3242 -0.1923 0.043 Uiso 1 1 calc R . .C21 C 0.4226(4) 0.1536(4) -0.2104(4) 0.0462(10) Uani 1 1 d . . . C22 C 0.5026(4) 0.1586(4) -0.0775(5) 0.0462(10) Uani 1 1 d . . . H22 H 0.5019 0.2227 -0.0175 0.055 Uiso 1 1 calc R . .C23 C 0.5807(4) 0.0677(4) -0.0391(4) 0.0433(10) Uani 1 1 d . . . H23 H 0.5931 0.0067 -0.0970 0.052 Uiso 1 1 calc R . .C24 C 0.6411(3) 0.0828(4) 0.1081(4) 0.0398(9) Uani 1 1 d . . . H24 H 0.6423 0.1533 0.1594 0.048 Uiso 1 1 calc R . .C25 C 0.8300(4) -0.1108(5) 0.3489(5) 0.0502(11) Uani 1 1 d . . . C26 C 0.8954(4) -0.0909(4) 0.4904(5) 0.0441(10) Uani 1 1 d . . . C27 C 0.9750(4) -0.0014(4) 0.5288(5) 0.0405(9) Uani 1 1 d . . . H27 H 0.9822 0.0570 0.4650 0.049 Uiso 1 1 calc R . .C28 C 1.0442(4) 0.0012(5) 0.6632(5) 0.0505(11) Uani 1 1 d . . . H28 H 1.0965 0.0623 0.6904 0.061 Uiso 1 1 calc R . .C29 C 0.9555(3) -0.1774(4) 0.7183(4) 0.0421(9) Uani 1 1 d . . . H29 H 0.9483 -0.2360 0.7819 0.051 Uiso 1 1 calc R . .C30 C 0.8865(3) -0.1796(3) 0.5848(4) 0.0337(8) Uani 1 1 d . . . H30 H 0.8341 -0.2407 0.5582 0.040 Uiso 1 1 calc R . .N1 N 0.8334(3) 0.4414(3) 0.3586(4) 0.0397(8) Uani 1 1 d . . .N2 N 0.7663(3) 0.5206(4) 0.2548(4) 0.0423(9) Uani 1 1 d . . .H2A H 0.777(4) 0.598(5) 0.259(5) 0.051 Uiso 1 1 d . . .N3 N 0.4603(3) 0.6964(3) -0.1372(3) 0.0392(8) Uani 1 1 d . . . N4 N 0.6918(3) -0.0162(3) 0.1548(4) 0.0424(8) Uani 1 1 d . . . N5 N 0.7800(3) -0.0023(3) 0.2797(3) 0.0368(8) Uani 1 1 d . . .N6 N 1.0342(3) -0.0891(4) 0.7569(4) 0.0491(9) Uani 1 1 d . . .O1 O 0.6774(2) 0.3578(3) 0.1322(3) 0.0434(7) Uani 1 1 d . . .O2 O 0.8172(2) -0.2090(3) 0.2914(3) 0.0440(7) Uani 1 1 d . . .loop_ 原子各向异性振动参数_atom_site_aniso_label_atom_site_aniso_U_11_atom_site_aniso_U_22_atom_site_aniso_U_33_atom_site_aniso_U_23_atom_site_aniso_U_13_atom_site_aniso_U_12C1 0.042(2) 0.052(3) 0.051(3) 0.004(2) 0.019(2) -0.006(2)C2 0.042(2) 0.048(2) 0.049(3) -0.011(2) 0.017(2) -0.0034(19)C3 0.043(2) 0.044(2) 0.043(2) -0.0022(18) 0.0214(19) 0.0020(18)C4 0.048(2) 0.042(2) 0.042(2) 0.0100(17) 0.0227(19) -0.0146(18)C5 0.037(2) 0.071(3) 0.035(2) -0.010(2) 0.0134(17) -0.014(2)C6 0.0332(18) 0.050(2) 0.046(2) -0.0088(19) 0.0149(17) 0.0070(18)C7 0.037(2) 0.043(2) 0.054(3) -0.014(2) 0.0238(19) 0.0071(18)C8 0.040(2) 0.041(2) 0.053(3) 0.0057(19) 0.0167(19) 0.0142(18)C9 0.051(2) 0.050(2) 0.0264(19) -0.0123(18) 0.0053(17) 0.003(2)C10 0.044(2) 0.036(2) 0.040(2) 0.0063(17) 0.0151(17) -0.0233(18)C11 0.054(3) 0.041(2) 0.038(2) -0.0013(18) 0.0163(19) -0.006(2)C12 0.0331(19) 0.038(2) 0.043(2) -0.0088(16) 0.0221(16) 0.0074(16)C13 0.042(2) 0.046(2) 0.040(2) -0.0042(18) 0.0172(18) -0.0041(19)C14 0.048(2) 0.042(2) 0.037(2) -0.0103(18) 0.0103(18) -0.0053(19)C15 0.041(2) 0.056(3) 0.032(2) -0.0133(18) 0.0092(17) -0.0076(19)C16 0.051(2) 0.045(2) 0.031(2) 0.0038(17) 0.0121(17) -0.005(2)C17 0.036(2) 0.046(2) 0.036(2) -0.0079(17) 0.0074(17) -0.0121(17)C18 0.047(2) 0.047(2) 0.043(2) -0.013(2) 0.0108(19) -0.0120(19)C19 0.049(2) 0.043(2) 0.034(2) -0.0051(17) 0.0128(18) -0.0036(19)C20 0.0386(19) 0.036(2) 0.037(2) 0.0037(16) 0.0175(16) -0.0144(16)C21 0.055(3) 0.051(3) 0.037(2) 0.0099(19) 0.0198(19) -0.004(2)C22 0.046(2) 0.044(2) 0.051(3) -0.0061(19) 0.018(2) 0.0147(19)C23 0.044(2) 0.045(2) 0.040(2) -0.0135(18) 0.0095(18) 0.0018(19)C24 0.0314(18) 0.052(2) 0.037(2) -0.0110(18) 0.0113(16) -0.0043(17)C25 0.050(2) 0.052(3) 0.054(3) 0.003(2) 0.022(2) 0.013(2)C26 0.047(2) 0.045(2) 0.049(3) 0.005(2) 0.028(2) 0.003(2)C27 0.038(2) 0.046(2) 0.044(2) 0.0012(18) 0.0225(18) 0.0001(17)C28 0.050(2) 0.063(3) 0.038(2) -0.009(2) 0.0126(19) -0.011(2)C29 0.040(2) 0.047(2) 0.044(2) -0.0077(18) 0.0202(18) 0.0067(18)C30 0.0285(16) 0.0339(19) 0.044(2) -0.0027(16) 0.0190(15) 0.0102(14) N1 0.0374(17) 0.0327(17) 0.0451(19) 0.0001(14) 0.0045(14) -0.0052(14)N3 0.0488(19) 0.0410(19) 0.0321(17) 0.0002(15) 0.0182(14) 0.0031(16)N4 0.055(2) 0.0406(19) 0.0303(17) -0.0039(15) 0.0093(16) -0.0081(17)N5 0.0338(17) 0.0399(18) 0.0350(18) -0.0011(14) 0.0064(14) -0.0151(14)N6 0.043(2) 0.062(2) 0.049(2) -0.0041(19) 0.0230(17) -0.0020(18)O1 0.0396(15) 0.0449(17) 0.0474(17) -0.0059(13) 0.0152(13) -0.0096(13)O2 0.0434(15) 0.0455(17) 0.0413(16) 0.0034(14) 0.0084(12) 0.0001(13)_geom_special_details 分子几何中需要说明的问题;All esds (except the esd in the dihedral angle between two l.s. planes)are estimated using the full covariance matrix. The cell esds are takeninto account individually in the estimation of esds in distances, anglesand torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.;loop__geom_bond_atom_site_label_1 分子中原子间键长列表_geom_bond_atom_site_label_2_geom_bond_distance_geom_bond_site_symmetry_2_geom_bond_publ_flagC1 C2 1.369(7) . ?C1 C6 1.385(7) . ?C1 H1 0.9300 . ?C2 C3 1.400(6) . ?C2 H2 0.9300 . ?C3 C4 1.394(6) . ?C3 H3 0.9300 . ?C4 C5 1.386(6) . ?C4 H4 0.9300 . ?C5 C6 1.397(7) . ?C5 H5 0.9300 . ?C6 C7 1.447(7) . ?C7 C8 1.375(7) . ?C7 H7 0.9300 . ?C8 C9 1.467(6) . ?C8 H8 0.9300 . ?C9 N1 1.273(5) . ?C9 H9 0.9300 . ?C10 O1 1.228(5) . ?C10 N2 1.432(5) . ?C11 C15 1.393(6) . ? C11 C12 1.400(6) . ? C12 C13 1.347(6) . ? C12 H12 0.9300 . ? C13 N3 1.390(6) . ? C13 H13 0.9300 . ? C14 N3 1.362(5) . ? C14 C15 1.390(7) . ? C14 H14 0.9300 . ? C15 H15 0.9300 . ? C16 C17 1.385(6) . ? C16 C21 1.415(7) . ? C16 H16 0.9300 . ? C17 C18 1.379(7) . ? C17 H17 0.9300 . ? C18 C19 1.405(6) . ? C18 H18 0.9300 . ? C19 C20 1.391(6) . ? C19 H19 0.9300 . ? C20 C21 1.391(6) . ? C20 H20 0.9300 . ? C21 C22 1.437(6) . ? C22 C23 1.383(6) . ? C22 H22 0.9300 . ? C23 C24 1.475(6) . ? C23 H23 0.9300 . ? C24 N4 1.287(6) . ? C24 H24 0.9300 . ? C25 O2 1.216(6) . ? C25 N5 1.439(6) . ? C25 C26 1.451(7) . ? C26 C27 1.385(6) . ? C26 C30 1.388(6) . ? C27 C28 1.391(7) . ? C27 H27 0.9300 . ? C28 N6 1.399(7) . ? C28 H28 0.9300 . ? C29 N6 1.368(6) . ? C29 C30 1.384(6) . ? C29 H29 0.9300 . ? C30 H30 0.9300 . ? N1 N2 1.442(5) . ? N2 H2A 0.86(5) . ?N5 H5A 0.90(5) . ?loop__geom_angle_atom_site_label_1 分子中原子间键角列表_geom_angle_atom_site_label_2_geom_angle_atom_site_label_3_geom_angle_geom_angle_site_symmetry_1_geom_angle_site_symmetry_3_geom_angle_publ_flagC2 C1 C6 119.7(5) . . ?C2 C1 H1 120.1 . . ?C6 C1 H1 120.1 . . ?C1 C2 C3 121.6(4) . . ?C1 C2 H2 119.2 . . ?C3 C2 H2 119.2 . . ?C4 C3 C2 118.4(4) . . ?C4 C3 H3 120.8 . . ?C2 C3 H3 120.8 . . ?C5 C4 C3 120.5(4) . . ?C5 C4 H4 119.8 . . ?C3 C4 H4 119.8 . . ?C4 C5 C6 119.9(4) . . ?C4 C5 H5 120.1 . . ?C6 C5 H5 120.1 . . ?C1 C6 C5 120.0(4) . . ?C1 C6 C7 116.7(5) . . ?C5 C6 C7 123.0(4) . . ?C8 C7 C6 120.0(4) . . ?C8 C7 H7 120.0 . . ?C6 C7 H7 120.0 . . ?C7 C8 C9 116.9(4) . . ?C7 C8 H8 121.5 . . ?C9 C8 H8 121.5 . . ?N1 C9 C8 111.1(4) . . ?N1 C9 H9 124.4 . . ?C8 C9 H9 124.4 . . ?O1 C10 N2 118.5(4) . . ?O1 C10 C11 119.7(4) . . ?N2 C10 C11 121.7(4) . . ?C15 C11 C12 119.1(4) . . ?C15 C11 C10 119.5(4) . . ?C12 C11 C10 120.7(4) . . ?C13 C12 H12 120.4 . . ?C11 C12 H12 120.4 . . ?C12 C13 N3 122.8(4) . . ? C12 C13 H13 118.6 . . ?N3 C13 H13 118.6 . . ?N3 C14 C15 121.0(4) . . ? N3 C14 H14 119.5 . . ?C15 C14 H14 119.5 . . ?C14 C15 C11 119.7(4) . . ? C14 C15 H15 120.1 . . ?C11 C15 H15 120.1 . . ?C17 C16 C21 119.6(4) . . ? C17 C16 H16 120.2 . . ?C21 C16 H16 120.2 . . ?C18 C17 C16 120.9(4) . . ? C18 C17 H17 119.6 . . ?C16 C17 H17 119.6 . . ?C17 C18 C19 119.6(4) . . ? C17 C18 H18 120.2 . . ?C19 C18 H18 120.2 . . ?C20 C19 C18 120.3(4) . . ? C20 C19 H19 119.9 . . ?C18 C19 H19 119.9 . . ?C21 C20 C19 119.9(4) . . ? C21 C20 H20 120.1 . . ?C19 C20 H20 120.1 . . ?C20 C21 C16 119.7(4) . . ? C20 C21 C22 116.2(4) . . ? C16 C21 C22 124.1(4) . . ? C23 C22 C21 119.7(4) . . ? C23 C22 H22 120.1 . . ?C21 C22 H22 120.1 . . ?C22 C23 C24 109.2(4) . . ? C22 C23 H23 125.4 . . ?C24 C23 H23 125.4 . . ?N4 C24 C23 109.7(4) . . ? N4 C24 H24 125.1 . . ?C23 C24 H24 125.1 . . ?O2 C25 N5 121.8(5) . . ? O2 C25 C26 124.4(4) . . ? N5 C25 C26 113.8(4) . . ? C27 C26 C30 120.0(4) . . ? C27 C26 C25 123.7(4) . . ?C26 C27 C28 119.9(4) . . ?C26 C27 H27 120.1 . . ?C28 C27 H27 120.1 . . ?C27 C28 N6 119.3(4) . . ?C27 C28 H28 120.3 . . ?N6 C28 H28 120.3 . . ?N6 C29 C30 120.1(4) . . ?N6 C29 H29 120.0 . . ?C30 C29 H29 120.0 . . ?C29 C30 C26 120.2(4) . . ?C29 C30 H30 119.9 . . ?C26 C30 H30 119.9 . . ?C9 N1 N2 108.8(4) . . ?C10 N2 N1 118.8(3) . . ?C10 N2 H2A 121(3) . . ?N1 N2 H2A 121(3) . . ?C14 N3 C13 118.2(4) . . ?C24 N4 N5 114.5(3) . . ?N4 N5 C25 117.7(4) . . ?N4 N5 H5A 108(3) . . ?C25 N5 H5A 108(3) . . ?C29 N6 C28 120.5(4) . . ?loop__geom_hbond_atom_site_label_D 分子内或分子间氢键列表_geom_hbond_atom_site_label_H_geom_hbond_atom_site_label_A_geom_hbond_distance_DH_geom_hbond_distance_HA_geom_hbond_distance_DA_geom_hbond_angle_DHA_geom_hbond_site_symmetry_AN2 H2A O2 0.86(5) 2.19(5) 3.049(5) 174(5) 1_565N5 H5A N6 0.90(5) 2.59(5) 3.427(5) 154(4) 2_554_diffrn_measured_fraction_theta_max 0.983 对精修时最大衍射角θ,衍射数据收集的完备率_diffrn_reflns_theta_full 27.74 精修时最大衍射角θ_diffrn_measured_fraction_theta_full 0.983 衍射数据的完备率_refine_diff_density_max 0.204 差值傅立叶图中最大残余电子密度峰值_refine_diff_density_min -0.289 差值傅立叶图中最消残余电子密度谷值_refine_diff_density_rms 0.039 差值傅立叶图中平均电子密度。

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2 ∂µ − m2 Bν (x) = 0,
(1)
where ∂µ = (∂/∂xm , ∂/i∂t, Bν (x) = (Bn (x), iB0 (x)). The corresponding Lagrangian for the neutral ﬁelds can be rewritten as follows (within unimportant divergent-type terms): L=− 1 2 (∂µ Bν )2 + m2 Bµ . 2 (2)
1
Canonical formalism
In the general case, without any constraints, the vector ﬁeld Bµ (x) realizes the (0, 0) ⊕ (1/2, 1/2) representation of the Lorentz group and describes four degrees of freedom which correspond to states with spins s = 0 and s = 1 (with three spin projections sz = 0, ±1). The massive ﬁeld functions Bµ (x) satisfy the Klein-Gordon-Fock equation
k + Bµ (k, t)eikx + Bµ (k, t)e−ikx ,
(10)
Hale Waihona Puke where L is the normalizing length so that the energy of a quantum is k0 = 2π/L and + the normalizing volume is V = L3 ; Bµ (k, t) is the Hermitian conjugated quantity. The time dependence of ﬁelds in the momentum space is Bµ (k, t) ∼ e−ik0 t ,
The Lagrangian (2) can be connected also with the Stueckelberg formulation of the vector ﬁeld [1]. A Lagrangian of the form (2) also was used [2] in a gauge-invariant formulation for a massive neutral vector ﬁeld. Eq.(1) can be represented in the form of ﬁrst-order equations [3] ∂ν ψµν − ∂µ ψ0 + m2 ψµ = 0, 1
1
E-mail: skruglov23@
ψµν = ∂µ ψν − ∂ν ψµ , ψ0 = ∂µ ψµ ,
(3)
with ψµ = Bµ , ψ0 = ∂µ Bµ . In the case m = 0 equations (3) are the generalized Maxwell equations with the gradient term (see [4-6]). Now we investigate the symmetry group of the four-component neutral vector ﬁeld Bµ which describes two spins 0, 1 (without the Lorentz condition, i.e. ∂µ Bµ = 0 (see Eq.(1)) with the Lagrangian (2) [7]. We call this ﬁeld “the Stueckelberg ﬁeld” [8]. ′ Let us consider the transformations Λ = (Λµν ) of the ﬁeld functions Bµ (x) = Λµν Bν (x), which belong to the group SO (3, 1) but which leave the coordinates xµ unchanged, i.e. x′µ = xµ . This is diﬀerent case from that of the Lorentz group where the coordinates xµ are transformed. It is easy to verify that the Lagrangian (2) is invariant under this group ′2 2 of symmetry transformations as Λµα Λµβ = δαβ and Bµ (x) = Bµ (x). In accordance with the Noether theorem [9,10] the invariance of the action integral under the group of the transformations under consideration one yields the law of conservation of the following antisymmetric tensor Sµ[αβ ] = Bβ ∂µ Bα − Bα ∂µ Bβ . (4) This tensor coincides with the density of spin momentum corresponding to the conservation law of spin momentum (4): ∂µ Sµ[αβ ] = 0. The invariance of the action integral (2) under the Lorentz transformations of the ′ coordinates x′µ = Lµν xν induces transformations of the ﬁeld functions Bµ (x′ ) = Lµν Bν (x) which lead to a conservation law for angular momentum Mµ[αβ ] [9,10], this being the sum of the orbital, Tµ[α xβ ] , and spin, Sµ[αβ ] , momenta: Tµν = − (∂µ Bα ) (∂ν Bα ) − Lδµν , Mµ[αβ ] = Tµ[α xβ ] + Sµ[αβ ] . (5) Therefore we also have here the law of conservation of orbital angular momentum: ∂µ Tµ[α xβ ] = 0. It should be noted that the Lorentz calibration ∂µ Bµ = 0 is not invariance under our group of symmetry (Λµν ). As the Lorentz calibration extracts the pure spin 1 of particles we come to the conclusion that the laws of conservation of the orbital, Tµ[α xβ ] , and spin, Sµ[αβ ] , angular momenta separately: ∂µ Tµ[α xβ ] = 0, ∂µ Sµ[αβ ] = 0 are due to the presence of two spins 0 and 1; i.e. multi-spin 0, 1. Now we consider a wider group of symmetry using the method of the Hamiltonian formalism. The generalized coordinates in this scheme are qµ (x) = Bµ (x). The density of the momenta found from Eq.(2) is given by πµ (x) = ∂ q µ (x) 2 ∂ L(x)
Abstract The internal symmetry group U(3,1) of the neutral vector ﬁelds with two spins 0 and 1 is investigated. Massless ﬁelds correspond to the generalized Maxwell equations with the gradient term. The symmetry transformations in the coordinate space are integro-diﬀerential transformations. Using the method of the Hamiltonian formalism the conservation tensors are found, and the quantized theory is studied. The necessity to introduce an indeﬁnite metric is shown. The internal symmetry group U (3, 1) being considered, after the transition to electrodynamics, reduces to the U (2) group. It is shown that the group of dual transformations is the subgroup of the group under consideration. All the linearly independent solutions of the equation for a free particle obtained in terms of the projection matrix-dyads.