Log mirror symmetry and local mirror symmetry

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4.1 Metal Surface
Although most metal surfaces are relaxed instead of recosntruction, some noble and near-noble fcc metals, Au, Ir, Pt and bcc transition metals, W and Mo, display recosntructions.
Trimer
2.3 Adatoms
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often on (111) surfaces
[110]
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4. Typical reconstruction surfaces
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（1）Surface: heterogeneous at microscopic scale （2）Surface processes: adsorption/desorption,
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Principle 2. A surface tends to compensate charges.
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Principle 3. A semiconductor surface tends to be insulating (or semiconducting).

IntJMechMaterDes2013

3D FE modeling of oblique shot peening using a new periodic cellFan Yang •Zhuo Chen •S.A.MeguidReceived:11August 2013/Accepted:11November 2013/Published online:23November 2013ÓSpringer Science+Business Media Dordrecht 2013Abstract Oblique incidence is often observed in the peening process due to the geometric complexity of some of the treated targets.Obliquity of the jet stream also exists as a result of the way the shots are propelled.It is therefore the purpose of this study to conduct a realistic 3D ﬁnite element (FE)analysis of the peening process involving a large number of shots impinging simultaneously at a rate sensitive target made from Ti-6Al-4V.A novel periodic cell model is developed and used to examine the effect of oblique incidence upon the induced plastic strains and residual stresses.Some aspects of the simulation are ﬁrst validated against published work in literature.The periodicity of the model is also examined and veriﬁed.A parametric study is further conducted to investigate the effect of various parameters involved in peening process using the newly proposed model.Several conclusions are drawn concerning the effect of incident angle,shot diameter and friction coefﬁcient upon the generated residual stress and plastic strain ﬁelds.Keywords Shot peening ÁOblique incidence ÁFinite element ÁPeriodic cell model ÁResidual stress1IntroductionShot-peening is a cold-working process accomplished by bombarding the surface of the component with small spherical shots at a relatively high impinging velocity.It is widely used to improve the fatigue life of metallic components in aerospace and automobile industries (Meguid 1986;Schulze 2006).The impinge-ment causes an indentation surrounded by a plastic region.After peening,a ﬁeld of compressive residual stress is left in the near surface layer due to inhomo-geneous elasto-plastic deformation.This compressive residual stress is highly beneﬁcial in retarding crack growth under cyclic loading conditions.Therefore,shot peening is a very useful treatment for improving the fatigue resistance of critical load bearing compo-nents such as gears,springs,compressor disc assem-blies,bogie beam in landing gears,cylinder head,connecting rods and crank shafts in automobiles.The shot peening process is governed by a signiﬁcant number of parameters (Wu et al.2012).These include size,density,shape and mechanical properties of the impinging shots,the geometry and mechanical proper-ties of the treated targets,shot mass ﬂow rate,impact velocity,incident angle,stand-off distance from the nozzle and exposure time.In order to control the effectiveness of peening treatment,it is necessary to establish quantitatively the relationship between these parameters and the resulting residual stress pattern.A number of experimental studies have been devoted to investigate the residual stresses resultingF.Yang ÁZ.Chen ÁS.A.Meguid (&)Mechanics and Aerospace Design Laboratory,University of Toronto,5King’s College Road,Toronto,ON M5S 3G8,Canada e-mail:meguid@mie.utoronto.caInt J Mech Mater Des (2014)10:133–144DOI 10.1007/s10999-013-9236-8from the peening process.Some authors focused on single shot impacts(Kobayashi et al.1998;Al-Hassani (1981).Kobayashi et al.(1998)found that the indentation shape and residual stress distribution caused by static compression are different from those caused by dynamic impact.A few methods,such as the hole-drilling(Kudryavtsev2008)and X-ray diffrac-tion(Noyan and Cohen1985;Prevey1991;Foss et al. 2013),have been developed to measure the residual stresses caused by shot-peening.On the other hand, Almen and Black(1963)introduced an indirect method to measure the arc-height resulting from peening a standard spring steel strip in order to quantify the peening intensity.This indirect method is, however,limited to the consistency of the treatment. The Almen strip height does not relate to the residual stress distribution(Guagliano2001)in a treated component made from another material.Computational simulation is showing an increasing power in investigating the shot-peening process. Schiffner and Helling(1999)investigated the effects of shot velocity,shot diameter and material parame-ters on the residual stress distribution and indentation depth using an axisymmetric model.(Meguid et al. 1999a,b)investigated the effects of shot velocity,size, shape and inter-space upon the development of plastic zone and residual stress.Hong et al.(2008a,b) compared the normalized residual stress proﬁles for different size,velocity,incident angle of the shots and the initial yielding and strain-hardening properties of targets.Kim et al.(2013)modeled the shots using different material models and explored the effects of material damping,element size,interfacial friction and incident angles upon the resulting residual stress ﬁeld.For the integration algorithm,some contribu-tions were made using quasi-static analysis(Meguid and Klair1985a,b;Li et al.1991).More efforts were made using explicit solvers to analyze the dynamic impact process(Meguid et al.1999a;Johnson1972; Klemenz et al.2009;Sheng et al.2012).For the material properties of target,some authors used rate insensitive models(Meguid et al.1999a;Edberg et al. 1995;Frija et al.2006).Others considered strain rate sensitivity in their constitutive models(Meguid et al. 2002;Mylonas and Labeas2011;Kim et al.2013). The results by Meguid et al.(2002)showed that the strain rate sensitivity of the target material cannot be neglected for modeling short duration impingements in shot peening.An important issue in shot peening is that the real target component often has a complex geometry (Rahimzadeh2009).Therefore oblique impingements are often involved in the shot peening process and thus need careful investigation.Single or a few shot impacts with oblique incident angles were investi-gated in some works.This includes the contributions made by Hong et al.(2008a,b),Kim et al.(2013)and Schwarzer et al.(2006).However,in real shot peening practice,each incidence event includes a large number of shots impinging on the target simultaneously.The adjacent shots would inﬂuence the residual stress distribution and make it different from that of a single or a few shots(Meguid and Klair1985a).For this purpose,Meguid et al.(2002,2007),Majzoobi et al. (2005)developed symmetry models of square base to describe the simultaneous impacts of multiple shots using mirror symmetry boundary conditions.Schiffner and Helling(1999),on the other hand,used a symmetry cell of isosceles triangle base to investigate the effect of adjacent shots.All these results showed that the effect of adjacent shots cannot be ignored. However,the symmetry cell models are only useful for simulating normal incidence impact;they are not applicable for the case of oblique impingements.So far,the study of simultaneous oblique impingements has not been covered in literature.It is for this reason that we conduct the current investigations.In this paper,a novel periodic cell model is developed for simulating multiple shots impinging obliquely and simultaneously at an elasto-plastic target made of strain-rate sensitive material.The paper is organized as follows.Following this brief introduction,we present the details of the proposed periodic cell model in Sect.2. Section3provides the results of a parametric study that addresses the effects of the pertinent parameters upon the performance of the shot peening treatment.The plastic zone development,the residual stress distribu-tion,and the surface morphology were analyzed and compared.In Sect.4,we conclude the paper.2Novel periodic cell model2.1Finite element modelingThe three-dimensional FE model was developed using the commercial code ABAQUS version6.11(2011). The explicit solver was adopted to calculate the134 F.Yang et al.dynamic problem.The situation envisaged is that of a large number of identical shots impinging simulta-neously at a metallic target at an identical incident angle h ,as shown in Fig.1a.The rigid shots are assumed to be positioned in a periodic array with a separation distance D between adjacent shots.Con-sidering periodicity and symmetry,a representative computational cell only needs to include half a shot,as depicted in Fig.1b.The coordinate system was assigned so that the z-axis is along the normal to the target surface and xz-plane is parallel to the shot trajectory.The origin was located at the middle of the edge of the top surface.The cell has a rectangular columnar geometry with dimensions of D /sin(h ),D /2and H along the three coordinates,respectively.The cell length along the x-axis changes with the incident angle in order to feature the same ﬂow density of the shot ﬂux through area perpendicular to the ﬂux direction.Considering the case involving shots closely adjoining each other,D was taken to be twice the shot radius R .The height of the cell was taken as fourth the shot radius,since this value is large enough to screen the effect of the bottom boundary (Meguid et al.2002).Instead of the symmetric boundary condition adopted in Refs.(Schiffner and Helling 1999;Meguid et al.2002;Meguid et al.2007),periodic boundary condition was used for the two lateral facets at the ends of the x-coordinate to simulate the periodically distributed simultaneous oblique impingements.The periodic boundary was implemented by coupling each degree of freedom (DOF)of the corresponding nodes on the two opposite faces so that the two faces would deform synchronously (ABAQUS Documentation 2011).The two lateral facets at the ends of the y-coordinate were constrained using symmetric boundary conditions.The nodes were constrained against all displacements at the bottom boundary.The material models used by Meguid et al.(2007)were also implemented in this paper.The target was modeled as Ti-6Al-4V with Young’s modulus E =114GPa,Poisson’s ratio v =0.342and density q =4,430kg/m 3.The initial yield stress is r 0=827MPa and the strain hardening parameters were extracted from the uniaxial stress–strain curve assuming isotropic hardening.The strain-rate sensitivity was accounted for using the data of Premack and Douglas (1995).These data were incorporated in the FE model by scaling the quasi-static stress–strain curve for different strain rates.The shots were modeled as rigid balls with density q shot =7,850kg/m 3and diameter d shot =0.36mm.The impinging velocity was assumed to be V =75m/s unless otherwise speciﬁed.The same value was also used by Hong et al.(2008a )and Meguid et al.(2002).The rigid shots were implemented in the FEmodelFig.1FE model:(a )Schematic plot of the simulated situation,and (b )Mesh and the coordinate system used3D FE modeling of oblique 135using an analytical rigid surface with an equivalent point mass an equivalent point rotational inertia positioned at its center.Convergence tests were conducted using different mesh sizes and the element size was ﬁnally chosen as 0.05R near the contact region of the target.Eight-node solid element with both full integration and reduced integration schemes were tested and were found to show no discernable difference in the resulting residual stress ﬁeld.Thus,the reduced integration scheme was used to save computational time.2.2Material dampingShot impingement typically produces high frequency stress waves,as can be seen in the displacement history in Fig.2.If these high frequency oscillations are not properly damped without affecting the low frequency component,the stress predictions will be in doubt.Figure 3shows the effect of numerical damp-ing of the high frequency component on the resulting stress ﬁeld (Kim et al.2013;Meguid et al.2002).In this paper,numerical damping was introduced in the following way.Firstly the shot impact process was simulated without material damping.This was followed by a continued simulation with material damping introduced.Since the damping speciﬁcations cannot be changed in the middle of a simulation in ABAQUS (2011),a two-job scheme was developed.The ﬁrst simulation job of 1.5l s duration was carried out without material damping for simulating the impact of shot.Then the obtained stress,strain,displacement and velocity ﬁelds at last time step were imported into the second job as the initial conditions for another run of2l s with material damping introduced.According to Meguid et al.(2002),the stiffness proportional damping coefﬁcient b was taken as 2910-9s.The mass proportional damping coefﬁcient a was taken to be 1H ﬃﬃﬃﬃ2E q q ,which is dependent on Young’s modulus,the density of the target and the cell height.Figure 2shows that in this scheme,unwanted residual oscilla-tions can be decayed rapidly.While Fig.3shows that the impact calculation was not much inﬂuenced.Consequently,the damping coefﬁcients were used in all the analyses conducted.Here and in the following studies,the residual stress is normalized by the initial yield stress r 0and the depth is normalized by the shot diameter d shot following Hong et al.(2008a ).2.3Validation of novel periodic cell model Since only one impinging event of simultaneous shots was simulated in this study,it is not appropriate to compare the obtained residual stress with that mea-sured in shot peening which involve a large number of impinging events.Therefore,we compared our results with the existing numerical studies in literature.Three papers were selected for this comparison (Meguid et al.2007;Hong et al.2008a ,b ).Firstly a comparison was made with the work by (Hong et al.2008a ,b )for a single shot impinging at a large plate.For this purpose,we created a simulation model with the same geometry,material,initial and boundary conditions as that used by Hong et al.It is noticed that the two papers by Hong et edtheFig.2Vertical displacement of the initial impinging point on the target surface for different dampingconditionsFig.3Residual stress r xx versus depth for different damping conditions.The horizontal line is a guide to eye indicating zero stress136 F.Yang et al.same simulation parameters except the contact prop-erties.In Hong et al.(2008a ),the impact contact is friction free,while in Hong et al.(2008b )a friction coefﬁcient of 0.2was used.The different contact properties resulted in different residual stress proﬁles along the depth direction beneath the impinging location in these two papers.There is a close match between our results and Hong’s results for both contact friction conditions,as shown in Fig.4.Second,a comparison was made with the work of Meguid et al.of multiple shots.A symmetry cell model was used by Meguid et al.(2007)to simulate a large number of shots impinging simultaneously at normal incidence.Here,we used our model of a periodic cell to reproduce their results.The periodic cell is twice the symmetry cell in Meguid et al.(2007).The top views of the two models are compared in Fig.5.Four series of multiple impingements were simulated.Each series includes four rows of multiple shots impinging simul-taneously at normal incident angle.The locations of thedepicted in Fig.5sequence forMeguid et al.(2007).along the depth between our (2007)as shown in obtained from our to those obtained in noted that a different was used in Meguid for the proposedSome additional validations were conducted to ensure that the proposed periodic cell model can accurately implement periodicity for the simultaneous oblique impingement.The following requirements should be satisﬁed.(i)Consistent results should be obtained at the coupled boundaries of the periodic cell,(ii)The generated results should be independent ofthe impinging location and,(iii)The periodic cell can be integrated into multiplecells.To check requirement (i),the residual stresses along the opposite vertical edges of the xz-plane were compared.The comparisons were made for both normal and oblique incidence at an angle of 60°.The results shown in Fig.7indicate that the residual stress proﬁles on the two coupled boundaries were very close.The maximum relative difference was less than 10%,occurred near the surface for the 60°incident angle.Fig.5Periodic and symmetry cells (Meguid et al.2007)with the numbers indicating the impinging sequence3D FE modeling of oblique 137To check requirement (ii),three simulations were carried out with the shot impinging at different locations of the top surface of the cell.Other parameters were kept unchanged.The angle of incidence was 60°.The impinging locations for the three tested simulations were respectively at (a)the ﬁrst quartile,(b)middle,and (c)the third quartile of the edge along x-axis.Figure 8compares the contour plots of the residual stress in xz-plane for the three cases.Figure 9compares the proﬁles of residual stress versus depth between the three cases along the two vertical lines.One is through the locationresidual stress shown as the black line in is the midline between two adjacent as the grey line.These results stress and displacement results for locations,validating the second (iii),a larger model that is 18cell model was created.The larger 9shots in a 393array.The length of the original model and the width the original model.Periodic boundary applied on the four lateral boundaries corresponding DOFs.Other parameters same as the original cell model.the contour plot of the residual stress of the larger paring Fig.10with Fig.8b,it shows that the larger model generated consistent residual stress as the original cell model.Figure 11compares the proﬁles of residual stress versus depth between the two models along the vertical lines indicated in Figs.10and 8b.3Effect of pertinent parametersThe proposed model is then used to investigate oblique and simultaneous impingements of a large number of shots to explore the effect of pertinent parametersFig.6Residual stress r xx proﬁles beneath the four locations indicated in Fig.6after four series of normal impingements:(a )current results,and (b )earlier results shown in Fig.12by Meguid et al.(2007)138 F.Yang et al.upon the induced residual stress and displacement.The investigated parameters include the incident angle h ,the shot diameter d shot and the coefﬁcient of friction l at the shot-target interface.For this purpose,a bench-mark case was chosen such that h =60°,V =75m/s,d shot =0.36mm,D =d shot and l =0.3.For all the simulations,the shot initially impinged at the coordi-nate origin,as shown in Fig.1b.3.1Effect of incident angleWe ﬁrst focus our attention on the effect of the incident angle.For this purpose ﬁve incident angles30°,45°,60°,75°and 90°.In the contours of the obtained residual the xz-plane.The magnitudes of the stresses are also marked at the location for each case.It is found that a angle results in a larger compressive residual stress.These tendencies to those obtained by Hong et al.(2008a ).stress r yy was also investigated.Fig-the contour plots of the induced residual the maximum values marked at the locations.Similar to the tendencies of angle leads to a larger compres-larger residual stresses,although the is different from r xx .Figure 14residual stresses r xx and r yy versus the incident angle h .It indicates that the magnitude of the maximum residual stress along the y-direction is larger than that along x-direction.The relative difference between the two stress components is larger for a smaller incident angle.Figure 15identiﬁes the locations of the maximum residual stress for different incident angles h .As expected,the x distance from the impinging location decreases while the depth increases,when the incident angle increases.These results indicate that normal incidence is the most effective scenario for the residual stress generation.The plastic strain and the surface morphology were also investigated.Figure 16compares the contourFig.8Residual stress r xx on xz-plane for the three simulations of different impinging locations3D FE modeling of oblique 139plots of the obtained equivalent plastic strain e eq in xz-plane for different incident angles.The magnitude of the maximum plastic strain was also marked at the corresponding location for each case.It is noted that the locations of maximum plastic strain do not coincide with those for maximum residual stresses.Figure 16indicates that as the incident angle increases,the depth of the plastic zone increases,while the magnitude of the maximum plastic strain decreases.Figure 17compares the surface proﬁleswith different incident angles.It shows incident angle resulted in a shallower pile-up residing ahead of the shot.of incident angle can be clearly seen viewpoint.The ﬁnal proportions of of energies are plotted versus the in Fig.18.It indicates that although a angle corresponds to a larger maxi-strain value,the plastic strain energy in as the incident angle increases.It both the translational kinetic energy kinetic energy of the rebound shot incident angle increases.Therefore,the is the most effective peening the plastic strain energy induced It is also found that the dissipated energy due to interfacial friction becomes larger when the incident angle is smaller.3.2Effect of shot diameterThe attention is now focused on the effect of shot diameter on the induced residual stress distribution.Four diameters were chosen for this investigation:0.36,0.72,1.08and 2.0mm.The dimensions of the FE model were changed proportionally,as stated in Sect.2.1.The normalized residual stress proﬁles areFig.10Residual stress contours in xz-plane for the larger model containing 9shots140F.Yang et al.compared in Fig.19along the depth through the maximum stress location.It indicates that the normal-ized residual stress proﬁle does not differ much for different shot sizes.Figure 20plots the locations of themaximum residual stress versus shot radius.It indi-cates that the distance from the impinging point is proportional to the shotdiameter.Fig.12Contour plots of the residual stress r xx in xz-plane for different incidentanglesFig.13Contour plots of the residual stress r yy in xz-plane for different incidentangles3D FE modeling of oblique 141Fig.16Contour plots of the equivalent plastic strain in xz-plane for different incidentangles142 F.Yang et al.3.3Effect of interfacial frictionWe also investigated the effect of the coefﬁcient of interfacial friction between the shot and the target upon the induced residual stressﬁeld.For this purpose,the coefﬁcient of Coulomb friction l was varied from0.0to 0.5.Three incident angles30°,60°and90°were investigated.In Fig.21,we plot the maximum residual stress r xx against the coefﬁcient of friction.Theﬁgure shows that for normal impingement,the maximum residual stress converges to a steady value for a friction coefﬁcient larger than0.2,a conclusion also made in literature(Meguid et al.2002;Kim et al.2013). However,for oblique impingement,the situation is more complex.The maximum residual stressﬁrstly decreases and then increases as the interfacial friction increases.For the30°incident angle,no convergence was observed within the considered friction range.4ConclusionsThe novel periodic cell model adopted in this article to treat the jet obliquity in shot peening led to the following conclusions:(i)A larger incident angle results in a larger residualstress and a larger compressive zone.On the other hand,a smaller plastic strain and a larger plastic zone were observed for a larger incident angle.This relates directly to the effective velocity components.(ii)An increase in the shot diameter does not effect much change in the magnitude of the maximumresidual stress.However,it increases the depth ofthe maximum residual stress and the compressedlayer.(iii)Unlike normal incidence where friction does not affect the residual stress proﬁle when l[0.2,in oblique shot stream impingement,frictiondoes affect the induced residual stressﬁeld. 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DOI: 10.1126/science.1083727, 1275 (2003);300 Science et al.Mingwei Chen Deformation Twinning in Nanocrystalline AluminumThis copy is for your personal, non-commercial use only.clicking here.colleagues, clients, or customers by , you can order high-quality copies for your If you wish to distribute this article to othershere.following the guidelines can be obtained by Permission to republish or repurpose articles or portions of articles): April 22, 2014 (this information is current as of The following resources related to this article are available online at/content/300/5623/1275.full.html version of this article at:including high-resolution figures, can be found in the online Updated information and services, /content/300/5623/1275.full.html#related found at:can be related to this article A list of selected additional articles on the Science Web sites /content/300/5623/1275.full.html#ref-list-1, 3 of which can be accessed free:cites 24 articles This article 293 article(s) on the ISI Web of Science cited by This article has been /content/300/5623/1275.full.html#related-urls 10 articles hosted by HighWire Press; see:cited by This article has been/cgi/collection/mat_sci Materials Sciencesubject collections:This article appears in the following registered trademark of AAAS.is a Science 2003 by the American Association for the Advancement of Science; all rights reserved. The title Copyright American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the Science o n A p r i l 22, 2014w w w .s c i e n c e m a g .o r g D o w n l o a d e d f r o mthat are normally FCC,such as gold,to maintain local,close-packed arrangements that are compatible with the constraints imposed by the surrounding environment. This result establishes a physically useful connection between dislocations and grain boundaries,the two most fundamental mi-crostructural elements underpinning the be-havior of polycrystalline materials.References and Notes1.A.P.Sutton,R.W.Ballufﬁ,Interfaces in CrystallineMaterials(Clarendon Press,Oxford,1995).2.J.Schiøtz,F.D.Di Tolla,K.W.Jacobsen,Nature391,561(1998).3.H.Van Swygenhoven,M.Spaczer,A.Caro,Acta Ma-ter.47,3117(1999).4.S.X.McFadden,R.S.Mishra,R.Z.Valiev,A.P.Zhilyaev,A.K.Mukherjee,Nature398,684(1999).5.H.Van Swygenhoven,Science296,66(2002).6.V.Yamakov,D.Wolf,S.R.Phillpot,A.K.Mukherjee,H.Gleiter,Nature Mater.1,45(2002).7.Y.Wang,M.Chen,F.Zhou,E.Ma,Nature419,912(2002).8.J.D.Rittner,D.N.Seidman,K.L.Merkle,Phys.Rev.B53,R4241(1996).9.W.Krakow,D.A.Smith,Ultramicroscopy22,47(1987).10.K.L.Merkle,Colloq.de Phys.51,C1-251(1990).11.F.Ernst et al.,Phys.Rev.Lett.69,620(1992).12.U.Wolf,F.Ernst,T.Muschik,M.W.Finnis,H.F.Fischmeister,Phil.Mag.A66,991(1992).13.K.L.Merkle,J.Phys.Chem.Solids55,991(1994).14.J.D.Rittner,D.N.Seidman,Phys.Rev.B54,6999(1996).15.D.L.Medlin,G.H.Campbell,C B.Carter,Acta Mater.46,5135(1998).16.D.L.Medlin,S.M.Foiles,D.Cohen,Acta Mater.49,3689(2001).17.T.Radetic,nc¸on,U.Dahmen,Phys.Rev.Lett.89,85502(2002).18.M.L.Jenkins,Philos.Mag.26,747(1972).19.T.J.Balk,K.J.Hemker,Phil.Mag.A81,1507(2001).20.R.D.Heidenreich,W.Shockley,in Report of a Con-ference on the Strength of Solids(Physical Society,London,1948),pp.57–75.21.F.C.Frank,J.H.van der Merwe,Proc.R.Soc.LondonA198,205(1949).22.N.Thompson,Proc.Phys.Soc.B66,481(1953).23.G.H.Campbell,D.K.Chan,D.L.Medlin,J.E.Angelo,C.B.Carter,Scripta Mater.35,837(1996).24.Here,we specify the boundary using the CSL notation(25),where⌺refers to the reciprocal density ofcoincident sites of two interpenetrating lattices re-lated by a rotation,␪.25.H.Grimmer,W.Bollmann,D.H.Warrington,ActaCrystallogr.A30,197(1974).26.D.G.Brandon,Acta Metall.14,1479(1966).27.C.B.Carter,D.L.Medlin,J.E.Angelo,ls,Mater.Sci.Forum207-209,209(1996).28.This work is supported by the U.S.Department ofEnergy,in part by the Ofﬁce of Basic Energy Sciences,Division of Materials Sciences,under contract DE-AC04-94AL85000.26February2003;accepted15April2003Deformation Twinning inNanocrystalline AluminumMingwei Chen,1*En Ma,2Kevin J.Hemker,1Hongwei Sheng,2Yinmin Wang,2Xuemei Cheng3We report transmission electron microscope observations that provide evi-dence of deformation twinning in plastically deformed nanocrystalline alumi-num.The presence of these twins is directly related to the nanocrystalline structure,because they are not observed in coarse-grained pure aluminum.We propose a dislocation-based model to explain the preference for deformation twins and stacking faults in nanocrystalline materials.These results underscore a transition from deformation mechanisms controlled by normal slip to those controlled by partial dislocation activity when grain size decreases to tens of nanometers,and they have implications for interpreting the unusual mechanical behavior of nanocrystalline materials.The extremely high strength and hardness of nanocrystalline materials relative to their coarse-grained counterparts suggest that normal dislocation activity—the dominant plastic deformation mode of ductile coarse-grained materials—is suppressed in nanocrys-talline grains.The resulting high strength of nanocrystalline materials may give rise to unique plastic deformation mechanisms that are not seen in coarse-grained materials(1–7).Twinning in aluminum,which has been suggested by recent molecular dynamics (MD)simulations(7,8),is an interesting case.Deformation twins have been observed in face-centered cubic(fcc)metals,such as copper and nickel(9–11),when deformed at subambient temperatures and/or high strain rates,but deformation twins have not been experimentally confirmed in single or poly-crystalline pure aluminum(7,8,11,12),evenwhen shock-loaded at low temperatures(13,14).The appearance of Shockley partial dis-locations at a crack tip of aluminum has beenregarded as an indication of deformationtwinning(15),but supporting evidence forthis claim has not been forthcoming.Nanocrystalline aluminum films withthickness ofϳ200andϳ400nm were pre-pared by physical vapor deposition of purealuminum(99.9%)onto oxidized(001)sili-con and sodium chloride substrates that werecooled with liquid nitrogen.The depositionwas performed at a pressure ofϳ5ϫ10Ϫ8torr and a deposition rate of5to10nm/min.To suppress columnar grain structures,weinterrupted the deposition for1min atϳ20-nm thickness intervals during film growth.Texture was negligible in these films,as in-dicated by x-ray diffraction analysis.The as-deposited films had grain sizes in the range of10to35nm(Fig.1A).High-resolution trans-mission electron microscope(HRTEM)ob-servations with a point-to-point resolution of0.2nm revealed that most of the nanograinswere separated by high-angle boundaries andthat no grain boundary phases were present inthese samples.Occasionally,growth twinswere observed with the twin boundary ap-pearing as a perfectly flat interface(Fig.1B).Such sharp interfaces have been previously1Department of Mechanical Engineering,2Depart-ment of Materials Science and Engineering,3Depart-ment of Physics and Astronomy,Johns Hopkins Uni-versity,Baltimore,MD21218,USA.*To whom correspondence should be addressed.E-mail:mwchen@Fig.1.Microstructure of as-prepared nanocrys-talline aluminum.(A)Bright-ﬁeld TEM micro-graphsh owing nanocrystalline grains withsizesranging from10to35nm.No dislocations ordeformation twins can be seen.(B)HRTEMimage of a growth͚3{111}twin boundary(marked by a white arrow).R E P O R T S SCIENCE VOL30023MAY20031275observed in deposited or annealed aluminum and have been referred to as the ͚3{111}twin boundary (16,17).The nanocrystalline aluminum films were deformed by microindentation and by manual grinding to allow the introduction of large plastic strains and to facilitate TEM observa-tions of the deformation defects.We chose these methods because the thin films cannot be tested in compression,and they fail with little plastic deformation in tension (18).The indented samples were thinned from the back using tripod polishing,dimpling,and finally low-temperature ion milling.The insert in Fig.2A shows a bright-field TEM micro-graph of a micro-indent with the fourfoldgeometry.No cracks can be seen,even at the corners of the indent,indicating that the for-mation of the indent is fully plastic.Around the edges of the indent,planar defects with two parallel flat boundaries were seen in a number of grains and were identified as de-formation twins.The width and orientation of the twin bands vary from grain to grain.The twinning seems to occur preferentially in smaller grains and propagates across the en-tire grain.An example is shown in the HRTEM micrograph of Fig.2B,together with a fast Fourier transform (FFT)pattern.The deformation twin can be recognized by the mirror symmetry between the band and the matrix in the atomic resolution image,in which the bright spots correspond to individ-ual atomic columns.The twin boundaries are determined to be parallel to one set of the {111}planes.In addition,the HRTEM image reveals that the deformation twin boundaries are several atomic planes thick,caused by twinning dislocations that are tilted relative to the electron beam and not clearly imaged.A large number of dislocations rather than de-formation twinning were found in coarse-grained aluminum deformed under the same indenter as shown in Fig.2C,confirming the grain-size dependence of the twinning mechanism.To rule out the possibility that deforma-tion twinning can only be induced under the very high pressures generated by a diamond indenter (19),we used a different deforma-tion scheme.Freestanding nanocrystalline aluminum films were released from sodium chloride substrates and manually ground into small fragments with an agate mortar and pestle in pure methanol for ϳ1min.This procedure is generally used to crush materials for TEM observations by applying complex stresses.These stresses are much lower than those generated by a sharp diamond indenter.The original film thickness was ϳ200nm,whereas the thickness of the fragments used for subsequent TEM observations was mea-sured to be less than 100nm by electron energy loss spectroscopy.The reduction in thickness appears to result from large plastic deformation,and the bright-field TEM mi-crograph in Fig.3A illustrates the features of the heavily deformed nanocrystalline alumi-num.The high density of planar defects that is shown in this figure is not seen in the as-deposited samples and is found to appear preferentially in smaller grains.Some of the defects were confirmed to be deformation twins by HRTEM.In these cases,multiple narrow twins often resided in a single grain,and the twinning planes were determined to be of the {111}type (Fig.3B).The FFT pattern of Fig.3B demonstrates the twin re-lationship among the bands and the matrix (Fig.3C).The multiple twins are highlighted in the Fourier-filtered image (Fig.3D)foraFig.2.(A )TEM micrographof deformation twins around an indent in nanocrystalline alu-minum.The inset shows the indent with the fourfold geometry.(B )HRTEM micrograph showing a deformation twin in (A)with parallel boundaries.This atomic resolution image cor-responds to the [110]direction and illustrates the mirror symmetry between the twin and the matrix.The morphological feature of the grain boundary at the twin band indicates that the twinning results in plastic deformation.The inset shows a FFT pattern conﬁrming the twin relationship between the band and the matrix.(C )Dislocations witha grain boundary (GB)around an indent in coarse-grained pure alumi-num and no evidence of deformationtwinning.Fig.3.TEM micrographs of nanocrystalline alu-minum deformed by manually grinding.(A )A high density of planar defects in a bright-ﬁeld image.Suchdefects are not observed in th e as-deposited nanocrystalline aluminum.(B )Multiple deformation twins and stacking faults in a [110]-oriented nanograin.(C )The FFT pat-tern showing the twin relationship among the narrow bands and matrix.(D )A Fourier-ﬁltered image from inside the white box in (B)for a close-up view of the deformation twins (T)and stacking faults (S).R E P O R T S23MAY 2003VOL 300SCIENCE 1276selected region in Fig.3B.Stacking faults,dislocations,and microbands were also ob-served in the samples.The TEM observations provide direct experimental evidence confirming the MD predictions of twinning during plastic defor-mation of nanocrystalline aluminum (7,8).Regarding the twinning mechanism of fcc materials,several models have been proposed in which deformation twins are created by stacking faults led by 1/6Ͻ112ϾShockley partial dislocations (20–23).The preference for twinning and stacking fault formation in nanocrystalline grains can be understood by comparing the critical shear stress needed to nucleate a perfect dislocation (1/2Ͻ110Ͼ)with an approximation of the source size equal to the grain size (D ),␶N ,with that required to initiate the Shockley partial (1/6Ͻ112Ͼ)twinning dislocation to generate stacking faults and deformation twins,␶p .Such a comparison can be made using for-mulations given by classical dislocation the-ory (22,23),where␶N ϭ2␣␮b ND(1)and␶P ϭ2␣␮b P D ϩ␥b P(2)Here ␮is the shear modulus (ϳ35GPa for aluminum),␥is the stacking fault energy [104to 142mJ/m 2for aluminum (7)],and b N and b P are the magnitudes of the Burgers vectors of the perfect dislocation and the Shockley partial dis-location,respectively.The parameter ␣reflects the character of the dislocation [␣ϭ0.5and 1.5for edge and screw dislocations,respectively (23)]and contains the scaling factor between the length of the dislocation source and the grain size.The grain boundaries are taken as dislocation sources,as predicted by computer simulations for nanocrystalline grains (6–8,12,24).When the grain size becomes smaller than a critical value,D c ,determined by equating Eqs.1and 2D c ϭ2␣␮(b N Ϫb P )b P␥(3)␶p becomes smaller than ␶N .Taking ␣ϭ1,the estimated D c is approximately 10to 15nm for aluminum.For simplicity,this model for nanocrystalline materials does not include the influence of elastic anisotropy,the small Peierls-Nabarro stress,localized stress con-centrations,and the interactions of disloca-tions with grain boundaries.Nevertheless,the predictions given by this simple model shed light on the experimentally observed trends in several ways.First,twinning becomes a pre-ferred deformation mode in aluminum with a grain size on the order of 10nm,which is consistent with our HRTEM observations of deformation twins in the grains with sizes ofϳ10to 20nm.The model also provides a physical explanation of the preferential gen-eration of partial dislocations,which results in the formation of stacking faults and defor-mation twins in nanocrystalline grains as sug-gested by computer simulations (6–8,12,24).Second,the ␶p estimated from Eq.2is much higher than ␶N in large aluminum grains,which is in agreement with the dom-inance of the normal dislocation plasticity in conventional aluminum.Third,for other fcc materials with lower ␥and higher ␮,the D c values are much larger and can be used to interpret the observation that deformation and growth twins are found in nanocrystalline copper and nickel (9,25–27)at D c values that are more than twice that of aluminum.Fourth,the generation of twin interfaces and stacking faults offers an alternative interpre-tation to dislocation pile-up at grain bound-aries to explain the continuous grain-size strengthening,as suggested by Eq.2,and the strain hardening of nanocrystalline materials (25–27).References and Notes1.J.R.Weertman et al .,Mater.Res.Soc.Bull.24,44(1999).2.I.A.Ovid’ko,Science 295,2386(2002).3.H.Van Swygenhoven,Science 296,66(2002).4.S.X.McFadden,R.S.Mishra,R.Z.Valiev,A.P.Zhilyaev,A.K.Mukherjee,Nature 398,684(1999).5.M.Murayama,J.M.Howe,H.Hidaka,S.Takaki,Science 295,2433(2002).6.J.Schiøtz,F.D.Di Tolla,K.W.Jacobsen,Nature 391,561(1998).7.V.Yamakov,D.Wolf,S.R.Phillpot,A.K.Mukherjee,H.Gleiter,Nature Mater.1,45(2002).8.V.Yamakov,D.Wolf,S.R.Phillpot,H.Gleiter,Acta Mater.50,5005(2002).9.J.Y.Huang,Y.K.Wu,H.Q.Ye,Acta Mater.44,1211(1996).10.T.H.Blewitt,R.R.Coltman,J.K.Redman,J.Appl.Phys.28,651(1957).11.J.A.Venables,in Deformation Twinning ,R.E.Reed-Hill,J.P.Hirth,H.C.Rogers,Eds.(Gordon &Breach,New York,1964),pp.77–116.12.K.W.Jacobsen,J.Schiøtz,Nature Mater.1,15(2002).13.G.T.Gray III,Acta Metall.36,1745(1988).14.G.T.Gray III,J.C.Huang,Mater.Sci.Eng.A145,21(1991).15.R.C.Pond,L.M.F.Garcia-Garcia,Inst.Phys.Conf.Ser.No.61(1981),p.495.16.M.Shamzuzzoha,P.A.Deymier,D.J.Smith,Philos.Mag.A 64,245(1991).17.Y.Champion,J.Bigot,Nanostruct.Mater.10,1097(1998).18.M.A.Haque,M.T.A.Saif,Scripta Mater.47,863(2002).19.E.B.Tadmor,ler,R.Phillips,M.Ortiz,J.Mater.Res.14,2233(1999).20.J.A.Venables,Philos.Mag.6,379(1961).21.J.B.Cohen,J.R.Weertman,Acta Metall .11,996(1963).gerlo ¨f,J.Castaing,P.Pirouz,A.H.Heuer,Philos.Mag.A 82,2841(2002).23.J.P.Hirth,J.Lothe,Theory of Dislocations (KriegerPublishing,Malabar,UK,ed.2,1992).24.H.Van Swygenhoven,P.M.Derlet,A.Hasnaoui,Phys.Rev.B 66,024101(2002).25.C.J.Youngdahl,J.R.Weertman,R.C.Hugo,H.H.Kung,Scripta Mater.44,1475(2001).26.F.Ebrahimi,G.R.Bourne,M.S.Kelly,T.E.Matthews,Nanostructured Materials 11,343(1999).27.K.S.Kumar,S.Suresh,M.F.Chisholm,J.A.Horton,P.Wang,Acta Mater.51,387(2003).28.We thank F.R.N.Nabarro for valuable discussion.This work was partially supported by the NSF (Divi-sion of Material Researchgrant 210215)and was conducted at the Electron Microscopy Center at Johns Hopkins University.The Johns Hopkins Electron Microscopy Facility is made possible by grants from the W.M.Keck Foundation and NSF.21February 2003;accepted 4April 2003Published online 24April 2003;10.1126/science.1083727Include this information when citing this paper.n -Type Conducting CdSe Nanocrystal SolidsDong Yu,Congjun Wang,Philippe Guyot-Sionnest*A bottleneck limiting the widespread application of semiconductor nanocrystal solids is their poor conductivity.We report that the conductivity of thin ﬁlms of n -type CdSe nanocrystals increases by many orders of magnitude as the occupation of the ﬁrst two electronic shells,1S e and 1P e ,increases,either by potassium or electrochemical doping.Around half-ﬁlling of the 1S e shell,a peak in the conductivity is observed,indicating shell-to-shell transport.Introducing conjugated ligands between nanocrystals increases the conductivities of these states to ϳ10Ϫ2siemens per centimeter.During the past decade,it has become appar-ent that solids of monodispersed nanocrystals provide the opportunity for developing mate-rials with novel properties (1,2).In particu-lar,semiconductor nanocrystals (3)offergreat promise for fabricating optoelectrical devices (4–6).In these “artificial atoms,”the inorganic cores allow precise tuning of the discrete electronic states by size confinement.To stabilize against sintering,retain solubili-ty,and maintain good optical properties,the surfaces are capped by organic ligands,as in the prototypical CdSe system (7).However,these ligands and traps on the nanocrystal surfaces are thought to inhibit electronicJames Franck Institute,University of Chicago,5640SouthEllis Avenue,Ch icago,IL 60637,USA.*To whom correspondence should be addressed.E-mail:pgs@R E P O R T S SCIENCE VOL 30023MAY 20031277。

(完整版)有机化学专业英语词汇(精)

有机化学专业英语词汇(精)acetal 醛缩醇acetal- 乙酰acid 酸-al 醛alcohol 醇-aldehyde 醛alkali- 碱allyl 烯丙基 [propenyl(丙烯基)] alkoxy- 烷氧基-amide 酰胺amino- 氨基的-amidine 脒-amine 胺-ane 烷anhydride 酐anilino- 苯胺基aquo- 含水的-ase 酶-ate 含氧酸的盐、酯-atriyne 三炔azo- 偶氮benzene 苯bi- 在盐类前表示酸式盐bis- 双-borane 硼烷bromo- 溴butyl 丁基-carbinol 甲醇carbonyl 羰基-carboxylic acid 羧酸centi- 10-2chloro- 氯代cis- 顺式condensed 缩合的、冷凝的cyclo- 环deca- 十deci 10-1-dine 啶dodeca- 十二-ene 烯epi- 表epoxy- 环氧-ester 酯-ether 醚ethoxy- 乙氧基ethyl 乙基fluoro- 氟代form 仿-glycol 二醇hemi- 半hendeca- 十一hepta- 七heptadeca- 十七hexa- 六hexadeca- 十六-hydrin 醇hydro- 氢或水hydroxyl 羟基hypo- 低级的，次hyper- 高级的，高-ic 酸的，高价金属-ide 无氧酸的盐，酰替胺，酐-il 偶酰-imine 亚胺iodine 碘iodo- 碘代iso- 异，等，同-ite 亚酸盐keto- 酮ketone 酮-lactone 内酯mega- 106meta- 间，偏methoxy- 甲氧基methyl 甲基micro- 10-6milli- 10-3mono- ( mon-) 一，单nano- 10-9nitro- 硝基nitroso- 亚硝基nona- 九nonadeca- 十九octa- 八octadeca- 十八-oic 酸的-ol 醇-one 酮ortho- 邻，正，原-ous 亚酸的，低价金属oxa- 氧杂-oxide 氧化合物-oxime 肟oxo- 酮oxy- 氧化-oyl 酰para- 对位，仲penta- 五pentadeca- 十五per- 高，过petro- 石油phenol 苯酚phenyl 苯基pico- 10-12poly- 聚，多quadri- 四quinque- 五semi- 半septi- 七sesqui 一个半sulfa- 磺胺sym- 对称syn- 顺式，同，共ter- 三tetra- 四tetradeca- 十四tetrakis- 四个thio- 硫代trans- 反式，超，跨thio- 硫代tri- 三trideca- 十三tris- 三个undeca- 十一uni- 单，一unsym- 不对称的，偏位-yl 基-ylene 撑(二价基，价在不同原子上) -yne 炔organic compounds 有机化合物compounds of carbon 碳化合物hydrocarbons and their derivatives 碳氢化合物及其衍生物organic chemistry 有机化学structure of molecule 分子结构chemical bond 化学键covalent bond 共价键hybrid orbital 杂化轨道bond length 键长bond angle 键角bond energy键能polarity 极性dissociation energy 离解能constitution构造contiguration构型conformation构象stereochemistry立体化学tetrahedral正四面体cis-顺trans-反isomerism同分异构现象isomer异构体stereoisomer立体异构constitutional isomer构造异构structural formula 结构式octet八隅体perspective 透视式eclipsed conformation重叠式构象staggered conformation交叉式构象newman projection纽曼投影式functional group 官能团chain compoud 链状化合物carbocyclic compound碳环化合物heterocyclic compound杂环化合物dipole-dipole interactions 偶极-偶极相互作用van der Waals forces 范德华力hydrogen bonding 氢键dipole moment偶极矩electronegativity 电负性physical property物理性质melting point熔点boiling point 沸点reaction mechanism反应机理homolysis均裂free redical自由基heterolysis异裂ionic type离子型electrophilic reagent亲电试剂electrophilic reaction亲电反应nucleophilic reagent亲核试剂nucleophilic reaction 亲核反应英文名汉文名Angular methyl group 角甲基Alkylidene group 亚烷基Allyl group 烯丙基Allylic 烯丙型[的]Phenyl group 苯基Aryl group 芳基Benzyl group 苄基Benzylic 苄型[的]Activating group 活化基团Chromophore 生色团Auxochrome 助色团Magnetically anisotropic group 磁各向异性基团Smally ring 小环Common ring 普通环Medium rimg 中环Large ring 大环Bridged-ring system 桥环体系Spiro compound 螺环化合物Helical molecule 螺旋型分子Octahedral compound 八面体化合物Conjugation 共轭Conjugated-system 共轭体系Acyl cation 酰[基]正离子Benzylic cation 苄[基]正离子Arenirm ion 芳[基]正离子Ketyl radical 羰自由基Radical ion 自由基离子Radical cation 自由基正离子Radical anion 自由基负离子Isomerism 异构[现象]Aci form 酸式Fluxional structure 循变结构Stereochemistry 立体化学Optical activity 光学活性Dextro isomer 右旋异构体Laevo isomer 左旋异构体Tetrahedral configuration 四面体构型Stereoisomerism 立体异构[现象] Asymmetric atom 不对称原子Asymmetric carbon 不对称碳Pseudoasymmetric carbon 假不对称碳Phantom atom 虚拟原子Homotopic 等位[的]Heterotopic 异位[的] Enantiotopic 对映异位[的] Diastereotopic 非对映异位[的] Configuration 构型Absolute configuration 绝对构型Chirality 手性Chiral 手性[的]Chiral center 手性中心Chiral molecule 手性分子Achiral 非手性[的]Fischer projection 费歇尔投影式Neoman projection 纽曼投影式D-L system of nomenclature D-L命名体系R-S syytem of nomenclature R-S命名体系Cahn-Ingold-Prelon sequence 顺序规则Symmetry factor 对称因素Plane of symmetry 对称面Mirror symmetry 镜面对称Enantiomer 对映[异构]体Diastereomer 非对映[异构]体Epimer 差向异构体Anomer 端基[差向]异构体Erythro configuration 赤型构型Erythro isomer 赤型异构体Threo configuration 苏型构型Threo isomer 苏型异构体Trigonal carbon 三角型碳Cis-trans isomerism 顺反异构E isomer E异构体Z isomer Z异构体Endo isomer 内型异构体Exo isomer 外型异构体Prochirality 前手性Pro-R group 前R基团Pro-S proup 前S基团Re face Re面Si face Si面Racemic mixture 外消旋混合物Racemic compound 外消旋化合物Racemic solid solution 外消旋固体溶液Meso compound 内消旋化合物Quasi recemate 准外消旋体Conformation 构象Conformational 构象分析Torsion angle 扭转角Rotamer 旋转异构体Anti conformation 反式构象Bisecting conformation 等分构象Anti periplanar conformation 反叠构象Synperiplanar conformation 顺叠构象Synclinal conformation 反错构象Synclinal conformation 顺错构象Eclipsed conformation 重叠构象Gauche conformation, skewcon-formation 邻位交叉构象Staggered conformation 对位交叉构象Steric effect 空间效应Steric hindrance 位阻Atropismer 阻转异构体Puckered ring 折叠环Conformational inversion 构象反转Chair conformation 椅型构象Boat conformation 船型构象Twist conformation 扭型构象Skew boat conformation 扭船型构象Half-chair conformation 半椅型构象Pseudorotation 假旋转Envelope conformation 信封[型]构象Axial bond 直[立]键Equatorial bond 平[伏]键Cisoid conformation 顺向构象Transoid conformation 反向构象Retention of configuration 构型保持Regioselectivity 区域选择性Regiospecificity 区域专一性Stereocelectivity 立体选择性Stereospecificty 立体专一性Conformer 构象异构体Conformational effect 构象效应Cram’s rube 克拉姆规则Prelog’rule 普雷洛格规则Stereochemical orientation 立体[化学]取向Conformational transmission 构象传递Homolog 同系物Ipso position 本位Ortho position 邻位Meta position 间位Para position 对位Amphi position 远位Peri position 近位Trigonal hybridization 三角杂化Molecular orbiral method 分子轨道法Valence bond method 价键法Delocalezed bond 离域键Cross conjugation 交叉共轭Vinylog 插烯物Mesomeric effect 中介效应Resonance 共振Resonance effect 共振效应Hyperconjugation 超共轭Isovalent hyperconjugation 等价超共轭No-bond resonance 无键共振Aromaticity 芳香性Aromatic sexter 芳香六隅Huckel’rule 休克尔规则Paramagnetic ring current 顺磁环电流Diamagnetic ring cruuent 抗磁环电流Homoaromaticity 同芳香性Antiaromaticity 反芳香性Alternant hydrocarbon 交替烃Non-alternant hydrocarbon 非交替烷Pericyclic reaction 周环反应Electrocyclic rearrangement 电环[化]重排Conrotatory 顺旋Disroatatory 对旋Cycloaddition 环加成Symmetry forbidden-reaction 对称禁阻反应Synfacial reaction 同面反应Antarafacial reaction 异面反应Mobius system 默比乌斯体系Leois structure 路易斯结构Coordinate-covalent bond 配位共价键Banana bond 香蕉键Pauling electronegativity scale 鲍林电负性标度Polarizability 可极化性Inductive effect 诱导效应Field effect 场效应Electrical effect 电场效应tautomerism 互变异构Tautomerization 互变异构化Keto-enol tautomerism 酮-烯醇互变异构Phenol-keto tautomerism 酚-酮互变异构Imine-enamine atutomerism 亚胺-烯胺互变异构Ring-chain tautomerism 环-链互变异构Valence tautomerism 价互变异构Ambident 两可[的]Solvent effect 溶剂效应Acid-base catalyxed reaction 酸性溶剂Basic solvent 碱性溶剂Dielectric constant 介电常数Solvated electron 溶剂化电子Acid-base catalyzed reaction 酸碱催化反应Conjugate base 共轭酸Conjugate base 共轭碱Therm odynamic acidity 热力学酸度Kinetic acidity 动力学酸度Electron donof-acceptor complex,EDAcomplex 电子给[体]受体络合物Host 主体Guest 客体Primary isotope effect 一级同位素效应Secondary isotope effect 二级同位数效应Inverse isotope effect 逆同位素效应Kinetic control 动力学控制Thermodynamic control 热力学控制Substrate 底物Intermediate 中间体Reactive intermediate 活泼中间体Microscopic reversibility 微观可逆性Hammond postulate 哈蒙德假说Linear free energy 线性自由能Non-bonded interaction 非键相互作用Torsional effect 扭转效应Pitzer strain 皮策张力Restricted rotation 阻碍旋转Eclipsing effect 重叠效应Eclipsing strain 重叠张力Small-angle strain 小角张力Large angle strain 大角张力Transannular interaction 跨环相互作用Transannular strain 跨环张力I strain 内张力F strain 前张力B strain 后张力Anomeric effect 端基异构效应Walden inversion 瓦尔登反转Racemization 外消旋化Isoinversion 等反转Isoracemization 等消旋Homochiral 纯手性[的] Mechanism 机理Unimolecular nucleophilic 单分子亲核取代Bimolecular nucleophilicsub-stitution 双分子亲核取代Bimolecular nucleophilicsubsti-tution(with allylic rearrange-ment) 双分子亲核取代（含烯丙型重排）Internal nucleophilicsubstiru-tion 分子内亲核取代Aromatic nucleophilicsubstitu-tion 芳香亲核取代Unimolecular electrophilicsub-stitution 单分子亲电取代Bimolecular electrophilicsubsti-tution 双分子亲电取代Nucleophile-assistedunimolecu-lar electrophilic substitution 亲核体协助单分子亲电取代Unimolecular elimination 单分子消除Bimolecular elimination 双分子消除Unimolecular elimination through the conjugate base 单分子共轭碱消除Bimolecular elimination through the conjugate base 双分子共轭碱消除Bimolecular elimination withfor-mation of a carbonyl group 双分子羰基形成消除Unimolecular acid-catalyzedacyl-oxygen cleavage 单分子酸催化酰氧断裂Bimolecular base-catalyzedacyl-oxygen cleavage 双分子碱催化酰氧断裂Unimolecular acid-catalyzedalkyl-oxygen cleavage 单分子酸催化烷氧断裂Bimllecular base-catalyzed al- kyl-oxygen cleavage 双分子碱催化烷氧断裂π-allyl complex mechanism π烯丙型络合机理Borderline mechanism 边理机理Homolysis 均裂Heterolysis 异裂Heterolytic michanism 异裂机理Counrer[gegen]ion 反荷离子Ion pair 离子对Carbocation 碳正离子Nonclassical carbocation 非经典碳正离子Carbanion 碳负离子Masked carbanion 掩蔽碳负离子Carbenoid 卡宾体Carbene 卡宾Nitrene 氮宾Carbine 碳炔Electrophilic addition 亲电加成Electrophile 亲电体Diaxial addition 双直键加成Markovnikov’s rube 马尔科夫尼科规则Anti-Markovnikov addition 反马氏加成Michael addition 迈克尔加成Substitution 取代Electrophilic substitution 亲电取代Addition-elimination mechanism 加成消除机理Electrophilic aromaticsubstitu-tion 亲电芳香取代Electron transfer 电子转移Electron-donating group 给电子基团Electron-Withdrawing group 吸电子基团Deactivating group 钝化基团Orinentation 取向Ortho-para directing group 邻对位定位基Meta directing group 间位定位基Ortho effect 邻位效应Partial rate factor 分速度系数Nucleophilic reaction 亲核反应Internal return 内返Nucleophilicity 亲核体Nucleophilicity 亲核性α-effect α-效应Backside attack 背面进攻Inversion 反转Umbrella effect 伞效应Push-pull effect 推拉效应Leaving group 离去基团Electrofuge 离电体Nucleofuge 离核体Phase-transfer catalysis 相转移催化Neighboring group participation 邻基基参与Neighboring proupassistance,anchimeric assistance 邻助作用Neighboring group effect 邻基效应Apofacial reaction 反面反应Briddgehead displacement 桥头取代Aryl action 芳正离子Benzyne 苯炔Zaitsev rule 札依采夫规则Anti-Zaitsev orientation 反札依采夫定向Hofmann’s rule 霍夫曼规则Bredt rule 布雷特规则Initiation 引发Anionic cleavage 负离子裂解Partial bond fixation 键[的]部分固定化02．3有机化学反应Alkylation 烷基化C- alkylation C-烷基化O- alkylation O-烷基化N-alkylation N-烷基化Silylation 硅烷[基]化Exhaustive methylation 彻底甲基化Seco alkylation 断裂烷基化Demethylation 脱甲基化Ethylation 乙基化Arylation 芳基化Acylation 酰化Formylation 甲酰化Carbalkoxylation 烷氧羰基化Carboamidation 氨羰基化Carboxylation 羧基化Amination 氨基化Bisamination 双氨基化Cine substitution 移位取代Transamination 氨基交换Hydroxylation 羟基化acyloxyation 酰氧基化Decarboxylative nitration 脱羧卤化Allylic halogenation 烯丙型卤化Dehalogenation 脱卤Nitration 硝化Decarboxylative nitration 脱羧硝化Nitrosation 亚硝化Sulfonation 磺化Chlorosulfonation 氯磺酰化Desulfonation 脱磺酸基Sulfenylation 亚磺酰化Sulfonylation 磺酰化Chlorosulfenation 氯亚磺酰化Chlorocarbonylation 氯羰基化Diazotization 重氮化Diazo transfer 重氮基转移Coupling reaction 偶联反应Diazonium coupling 重氮偶联Cross-coupling reaction 交叉偶联反应1,4-addition 1，4-加成Conjugate addition 共轭加成Dimerization 二聚Trimefization 三聚Additive dimerization 加成二聚sulfurization 硫化Selenylation 硒化Hydroboration 硼氢化Oxyamination 羟氨基化Insertion 插入carbonylation 羧基化Hydroformylation 加氢甲酰基化Hydroacylation 加氢酰化Oxo process 羰基合成Decarbonylation 脱羰Hydrocarboxylation 氢羧基化Homologization 同系化Cyanoethylation 氰乙基化Decyanoethylation 脱氰乙基Ring clsure 环合Diene synthesis 双烯合成Dienophile 亲双烯体Endo addition 内型加成Exo addition 外型加成Diels-Alder reaction 第尔斯-尔德反应Retro Diels-Alder reaction 逆第尔斯-阿尔德反应Ene synthesis 单烯合成Anionic cycloaddition 负离子环加成Dipolar addition 偶极加成- elimination -消除- elimination -消除- elimination -消除-elimination -消除Dehydrohalogenation 脱卤化氢Deamination 脱氨基Pyrolytic elimination 热解消除Elimination-addition 消除-加成Decarboxylation 脱羧Decarboxamidation 脱酰胺Decyanation 脱氰基Alkylolysis,alkyl cleavage 烷基裂解Acylolysis,acyl cleavage 酰基裂解Flash pyrolysis 闪热裂Fragmentation 碎裂Chiletropic reaction 螯键反应Chelation 螯环化Esterification 酯化Transesterification 酯交换Saponification 皂化Alcoholysis 醇解Ethanolysis 乙醇解Cyanomethylation 氰甲基化Aminomethylation 氨甲基化Hydroxymethylation 羟甲基化Hydroxyalkylation 羟烷基化Cholromethylation 氯甲基化Haloalkylation 卤烷基化Transacetalation 缩醛交换Enolization 烯醇化Haloform reaction 卤仿反应Condensation 缩合Aldol condensation 羟醛缩合Cross aldol condensation 交叉羟醛缩合Retrograde aldol condensation 逆羟醛缩合Acyloin condensation 偶姻缩合Cyclization 环化Annulation,annelation 增环反应Spiroannulation 螺增环Autoxidation 自氧化Allylic hydroperoxylation 烯丙型氢过氧化Epoxidation 环氧化Oxonolysis 臭氧解Electrochemical oxidation 电化学氧化Oxidative decarboxylation 氧化脱羧Aromatization 芳构化Catalytic hydrogenation 催化氢化Heterogeneous hydrogenation 多相氢化Homogeneous hydrogenation 均相氢化Catalytic dehydrogenation 催化脱氢Transfer hydrogenation 转移氢化Hydrogenolysis 氢解Dissolving metal reduction 溶解金属还原Single electron transfer 单电子转移Bimolecular reduction 双分子还原Electrochemical reduction 电化学还原Reductive alkylation 还原烷基化Reductive acylation 还原酰化Reductive dimerization 还原二聚Deoxygenation 脱氧Desulfurization 脱硫Deselenization 脱硒Mitallation 金属化Lithiation 锂化Hydrometallation 氢金属化Mercuration 汞化Oxymercuration 羟汞化Aminomercuration 氨汞化Abstraction 夺取[反应]Internal abstraction 内夺取[反应] Rearrangement 重排Prototropic rearrangement 质了转移重排Double bond migration 双键移位Allylic migration 烯丙型重排Allylic migration 烯丙型迁移Ring contraction 环缩小[反应] Ring expansion,ring enlargement 扩环[反应]-ketol rearrangement -酮醇重排Pinacol rearrangement 频哪醇重排Retropinacol rearrangement 逆频哪醇重排Semipinacol rearrangement 半频哪醇重排Benzilic rearrangement 二苯乙醇酸重排Acyl rearrangement 酰基重排Migratory aptitude 迁移倾向Transannular insertion 跨环插入Transannular rearrangement 跨环重排Migration 迁移Prototropy 质子转移Cationotropic rearrangement 正离子转移重排Anionotropy 负离子转移Anionotropic rearrangement 负离子转移重排Sigmatropic rearrangement -迁移重排Homosigmatropic rearrangement 同迁移重排Electrophilic rearrangement 亲电重排Photosensitization 光敏化Forbidden transition 禁阻跃迁photooxidation 光氧化Photoisomerization 光异构化Photochemical rearrangement 光化学重排2．4 有机化合物类名Aliphatic compound 脂肪族化合物Hpdrocarbon 碳氢化合物Alkane 烷Wax 蜡Paraffin wax 石蜡Alkene 烯Alkyen 炔Acetylide 炔化物Active hydrogen compounds 活泼氢化合物Carbon acid 碳氢酸Super acid 超酸Diene 双烯Triene 三烯Allene 丙二烯Ccumulene 累积多烯Enyne 烯炔Diyne 二炔Alkyl halide 卤代烷Alcohol 醇Homoallylic alcohol 高烯丙醇Ether 醚Epoxide 环氧化物Cellosolve 溶纤剂Crown ether 冠醚Netro compound 硝基化合物Amine 胺Quaternaryammonium com-pound 季铵化合物Amine oxide 氧化胺Diazoalkane 重氮烷Mercaptan 硫醇Sulfonic acid 磺酸Sulfoxide 亚砜Sulfone 砜Aldehyde 醛Detone 酮Aldehyde hydrate 醛水合物Ketone hydrate 酮水合物Hemiacetal 半缩醛Acetal 缩醛Ketal 缩酮Dithiane 二噻烷Aminal 缩醛胺imine 亚胺Aldimine 醛亚胺Oxime 肟Aldimine 醛肟Oxime 亚硝基化合物aldoxime 硝酮Hydrazone 腙Azine 嗪Semicarbazone 缩氯基脲Cyanohydrin 羟腈Pinacol 频哪醇Enol 烯醇Enol ether 烯醇醚Enol ester 烯醇酯Enamine 烯胺Ynamine 炔胺Mannich base 曼尼希碱Carboxylic acid 羧酸Ester 酯orthoester 原酸酯Acyl halide 酰卤Acyl fluoride 酰氟Acyl chloride 酰氯Acyl rtomide 酰溴Acyl iodide 酰碘Carbobenzoxy chloride 苄氧甲酰氯Acyl tosylate 酰基对甲苯磺酸酐Ketene 乙烯酮Peracid 过酸Perester 过酸酯Acyl peroxide 酰基过氧化物Nitrile 腈Nitrile oxide 氧化腈Isonitrile 异腈Amide 酰胺Imide 二酰亚胺N-bromo compound N-溴化物Hydrazide 酰肼Acyl azide 酰叠氮Amidine 脒Keto ester 酮酸酯Acyl cyanide 酰腈Carbon suboxide 二氧化三碳Glycidic acid 环氧丙酸Carbammic acid 氨基甲酸Carbamate 氨基甲酸酯Urea 脲Cyanamide 氨腈Carbodiimide 碳二亚胺Allophanate 脲基甲酸酯Thioester 硫代酸酯Thiol acid 硫羰酸Lactone 内酯Lactol 内半缩醛Macrolide 大环内酯Amino acid 氨基酸Zwitterions 两性离子Inner salt 内盐Betaine 甜菜碱Lactam 内酰胺Hydantion 乙内酰脲Peptide 肽Glycol 二醇Aldol 羟醛Acyloin 偶姻Carbohydrate 碳水化合物Aldose 醛糖Ketose 酮糖Furanose 呋喃糖Pyranose 吡喃糖Glycoside 糖苷Glucoside 葡[萄]糖苷Aglycon 苷元Saccharide 糖类Oligosaccharide 寡糖Polysaccharide 多糖Alditol 糖醇Osazone 脎Alicyclic compound 脂环化合物Cycloalkene 环烷Spirane 环烯Cage compound 螺烷Propellane 笼型化合物Rotazane 螺桨烷Catenane 轮烷Rused ring 索烃11。

J. Photochem. and Photobiol. C; Photochem. Rev. 2004, 5, 169-182

Journal of Photochemistry and Photobiology C:Photochemistry Reviews5(2004)169–182ReviewDiarylethene as a photoswitching unitKenji Matsuda,Masahiro Irie∗Department of Chemistry and Biochemistry,Graduate School of Engineering,Kyushu University,6-10-1Hakozaki,Higashi-ku,Fukuoka812-8581,JapanAccepted9July2004AbstractPhotochromic compounds reversibly change not only the absorption spectra but also their geometrical and electronic structures.The molecular structure changes induce physical property changes of the molecules such asﬂuorescence,refractive index,polarizability,electrical conductivity,and magnetism.In this review,among the physical properties that can be photoswitched by using diarylethenes as a photoswitching unit,ﬂuorescence,electrical conductivity,and magnetism are featured.©2004Japanese Photochemistry Association.Published by Elsevier B.V.All rights reserved.Keywords:Photochromism;Photoswitching;Diarylethene;Metal complex;Fluorescence;Phosphorescence;FRET;Single molecule;Electrical conductivity; Molecular magnetismContents1.Introduction (170)2.Photoswitching ofﬂuorescence (170)2.1.Photoswitching ofﬂuorescence (170)2.2.Emission from metal complexes (172)2.3.Fluorescence resonance energy transfer(FRET) (173)2.4.Photochromism at the single-molecule level (174)3.Photoswitching of electrical conductivity (176)4.Photoswitching of magnetism (177)4.1.Intramolecular magnetic interaction in diarylethenes (177)4.2.Photoswitching of magnetism using a diarylethene (177)4.3.Photoswitching using an array of diarylethenes (180)5.Conclusions (181)Acknowledgements (181)References (181)∗Corresponding author.Fax:+81926423568.E-mail address:irie@cstf.kyushu-u.ac.jp(M.Irie).1389-5567/$20.00©2004Japanese Photochemistry Association.Published by Elsevier B.V.All rights reserved.170K.Matsuda,M.Irie/Journal of Photochemistry and Photobiology C:Photochemistry Reviews5(2004)169–182 1.IntroductionPhotochromism refers to a reversible phototransformationof a chemical species between two forms having different ab-sorption spectra[1–4].Photochromic compounds reversiblychange not only the absorption spectra but also their geo-metrical and electronic structures.The molecular structurechanges induce physical property changes of the molecules,such asﬂuorescence,refractive index,polarizability,elec-trical conductivity,and magnetism.Photoswitching of thesephysical properties can be accomplished by appropriate de-sign of the molecules.By feeding back the evaluation of thephysical properties to the molecular design,more sophisti-cated photoresponsive molecular systems can be constructed.Diarylethenes with heterocyclic aryl groups are wellknown as thermally irreversible,highly sensitive,and fatigue-resistant photochromic compounds[5,6].The photochromicreaction is based on a reversible transformation between theopen-ring isomer,with a hexatriene structure,and the closed-ring isomer,with a cyclohexadiene structure,according to theWoodward–Hoffmann rule(Scheme1).While the open-ringisomer1a is colorless in most cases,the closed-ring isomerhas a color of yellow,red,or blue,depending on the molecularstructure.The difference in color is due to the difference in the ge-ometrical and electronic structures.In the open-ring isomer,free rotation is possible between the ethene moiety and thearyl group.Therefore,the open-ring isomer is non-planar andthe␲-electrons are localized in the two aryl groups.More-over,the open-ring isomer has two conformations,with thetwo rings in mirror symmetry(parallel conformation)andin C2symmetry(antiparallel conformation)[7].The photo-cyclization reaction can proceed only from the antiparallelconformation(Scheme2).On the other hand,the closed-ring isomer has a planar structure and there exist two enan-tiomers(R,R and S,S),originating from two asymmetric car-bon atoms.The closed-ring isomer is regarded as an alternatepolyene and the␲-electrons are delocalized throughout themolecule.These structure differences resulted in the differ-ence in the physical properties.For example,the closed-ringisomer has a higher polarizability,because the closed-ringisomer has more delocalized␲-electrons[8,9].Photochromic materials have the characteristic featurethat the function is based on the structure changes of singlemolecules.Therefore,photochromic reactions can be usednot only to control the bulk physical properties but also toswitch single-molecule devices.As components of molec-ular electronics,it is desirable to develop various typesofScheme2.Conformations of diarylethenes.molecular switching devices[10–12].In this sense,the pho-tochromic diarylethene is one of the most promising candi-dates for applications in molecular electronics.In this review,among the various physical properties which can be photoswitched by using diarylethenes as a pho-toswitching unit,molecules which changeﬂuorescence,elec-trical conductivity,and magnetism upon photoirradiation aredescribed.2.Photoswitching ofﬂuorescence2.1.Photoswitching ofﬂuorescenceFor the application of photochromic compounds in record-ing media,non-destructive readout capability is one of themost important requirements.In a conventional transmit-tance readout method,the readout light always induces a pho-tochromic reaction to some extent.Therefore,the recordedinformation is destroyed after many readout operations.Onthe other hand,aﬂuorescence readout method is more sensi-tive than the transmittance readout method.When veryweakK.Matsuda,M.Irie /Journal of Photochemistry and Photobiology C:Photochemistry Reviews 5(2004)169–182171Scheme 4.readout power is used,the destruction of the recorded infor-mation can be minimized [13,14].Several ﬂuorescent photoswitching molecules have been synthesized.Diarylethene 2is a ﬂuorescent photoswitching molecule synthesized by Tsivgoulis and Lehn (Scheme 3)[15,16].The open-ring isomer 2a is converted to the closed-ring isomer 2b in methanol by irradiation with UV light (λ<400nm)with conversion of 92%,and the closed-ring isomer 2b returns to the open-ring isomer 2a by irradiation with vis-ible light (λ>600nm)quantitatively.The absorption band at 459nm,which appeared in both isomers,is assigned to the absorption of the pyridyl–dithienothiophene–thiophene moiety.When excited in the 400–500nm region,the open-ring isomer 2a showed ﬂuorescence with an emission max-imum at 589nm,but the closed-ring isomer 2b showed al-most no ﬂuorescence (less than 3%of that of the open-ring isomer).The open-ring isomer is in the “ON”state and the closed-ring isomer is in the “OFF”state.When the ﬂuores-cence can be detected without inﬂuencing the ratio of the two isomers,the ﬂuorescence readout method becomes non-destructive.Actually,both cyclization and cycloreversion re-actions hardly took place when the molecule was excited with a narrow range of the excitation wavelength (450–460nm).The molecule has quasi-non-destructive capability.Diarylethene 3,with a 4-formylthiophene group,exhibits a ﬂuorescence-photoswitching property (Scheme 4)[17].By irradiation with 301nm light,the open-ring isomer 3a showed ﬂuorescence,with an emission maximum at 420nm,but the closed-ring isomer 3b did not show any ﬂuorescence.Triphenylimidazole is known as a compound with a high ﬂuorescence quantum yield (48%).Diarylethene 4,with a triphenylimidazole group,was synthesized (Scheme 5)[18].The open-ring isomer 4a showed ﬂuorescence at 390and 410nm,with a ﬂuorescence quantum yield of 7.7%when excited at 313nm,but the closed-ring isomer 4b did not show any ﬂuorescence.In spite of the relatively high ﬂuorescence yield,4a showed a high cyclization quantum yield of 0.49.The cycloreversion quantum yield was 1/10of that of the cyclization reaction.Osuka et al.reported the synthesis and ﬂuorescence be-havior of diarylethene 5,with a tetraphenylporphyrin moiety (Scheme 6)[19].The open-ring isomer 5a showed ﬂuores-cence at 650and 717nm when excited at 420nm,but the closed-ring isomer 5b showed only weak ﬂuorescence.The energy transfer from the excited porphyrin to the closed-ring isomer of the diarylethene prohibits the ﬂuorescence.The conversion from the open-to the closed-ring isomers under irradiation with 330nm light was 75%,and the cyclization and cycloreversion quantum yields were determined to be 4.3×10−2and 1.8×10−3,respectively.Bis(diarylethene)6has two diarylethenes and one ﬂuo-rescent bis(phenylethynyl)anthracene (Scheme 7)[20].The ﬂuorescence quantum yield of bis(phenylethynyl)anthracene was determined to be 0.83for the open-ring isomer 6a and 0.001for the closed-ring isomer 6b .Relatively large ﬂuores-cence switching was observed in this molecule.The open-ring isomer 6a showed laser emission by excitation with 337.1nm laser pulses and the laser emission intensity could be reversibly switched by alternative irradiation with UV and visible light.Tian et al.reported ﬂuorescence-photoswitching systems using tetraazaporphyrin–diarylethene hybrid 7(Scheme 8)[21].This molecule,having four diarylethene units,exhibits a photochromic property by irradiation with UV and visible light.It was suggested that the cyclization reaction occurs at two opposite positions of the tetraazaporphyrin.The open-ring isomer 7a is ﬂuorescent,but the closed-ring isomer 7b is non-ﬂuorescent.The near-IR emission maximum of the172K.Matsuda,M.Irie /Journal of Photochemistry and Photobiology C:Photochemistry Reviews 5(2004)169–182Scheme 6.open-ring isomer was observed at 689nm when excited at 480nm.The detailed mechanism of the ﬂuorescence from 1,2-bis(3-methyl-2-thienyl)ethene 8a was studied in solution as well as in the single-crystalline phase (Scheme 9)[22].The characteristic ﬂuorescence of the crystal at 520nm was attributed to the ﬂuorescence from aggregates of the di-arylethene molecules in the crystal.Similar bathochromic ﬂuorescence was also observed in the concentrated hexane solution of the molecule.The structure of the aggregatewasestimated from the ﬂuorescence anisotropy and X-ray crys-tallographic analysis of the single crystal.The closed-ring isomer did not show any ﬂuorescence.Kryschi and co-workers reported the ﬂuorescence dynam-ics on an anthracene-substituted diarylethene 9a (Scheme 10)[23].The non-reacting parallel conformer is suggested to con-tribute to the ﬂuorescence.2.2.Emission from metal complexesBranda and co-workers reported phosphorescence-switching molecules with transition metals (Scheme 11)[24,25].In molecule 10a ,a diarylethene with two pyridyl groups is axially coordinated to ruthenium porphyrins.The open-ring isomer 10a is converted to the closed-ring isomer 10b with a conversion of 95%by irradiation with 365nm light.The closed-ring isomer 10b is converted back to the open-ring isomer completely by irradiation with visible light (470nm <λ<685nm).The open-ring isomer 10a showed phosphorescence at 730nm when excited with visible light (400nm <λ<480nm).On the other hand,the closed-ring isomer 10b did not show any phosphorescence.Con-veniently,both the open-and closed-ring isomers of the cen-tral bispyridyl diarylethene unit are transparent in this re-gion.Therefore,irradiation with light in the wavelength range (400nm <λ<480nm)scarcely induces photochemical in-terconversion in either direction.Non-destructive readout isK.Matsuda,M.Irie /Journal of Photochemistry and Photobiology C:Photochemistry Reviews 5(2004)169–182173Scheme8.Scheme 9.Fern´a ndez-Acebes and Lehn developed a novel di-arylethene tungsten complex 11,in which the closed-ring isomer shows stronger ﬂuorescence than the open-ring iso-mer (Scheme 12)[26].When excited at 240nm,the ﬂuores-cence quantum yield of the closed-ring isomer 11b was 0.15,while the ﬂuorescence quantum yield of the open-ring iso-mer 11a was only 0.03.Irradiation with 240nm light did not induce any photochromic reaction in either direction,so that non-destructive readout can be achieved in this system.Diarylethene 12is also reported to show emission from the closed-ring isomer (Scheme 13)[27].The open-ring isomer 12a showed ﬂuorescence at 450nm,with ﬂuorescence quan-tum yield of 1.1%,while the ﬂuorescence maximum shifted to 650nm when 12a converted to 12b .The ﬂuorescence at 650nm was ascribed to that from excited 12b .De Cola and co-workers reported the emission behavior of diarylethene Ru and Os complexes 13(Scheme 14)[28].The emission from the triplet metal-to-ligand charge-transfer (3MLCT)state was observed at 630and 759nm for Ru and Os complexes,respectively.Interestingly,in the Ru complex,a photocyclization reaction of the diarylethene unitthrougha 3MLCT state was observed.Neither closed-ring isomer showed any emission.2.3.Fluorescence resonance energy transfer (FRET)FRET is widely used for imaging and analysis of biological reaction processes.Jares-Erijman and co-workers reported photoswitchable FRET systems using diarylethenes (Scheme 15)[29].The FRET systems are useful to analyze the reaction kinetics in detail in biological systems.In these systems,Lucifer Yellow is used as a ﬂuorescence donor moiety and is connected to a diarylethene photochromic pound 14shows a typical example.The closed-ring isomer of the diarylethene unit in 14b has an absorption band overlapping the emission band of the donor.When the diarylethene is in the open-ring form,the donor ﬂuorescence is not perturbed by the diarylethene unit and gives strong acceptor-free ﬂuorescence.On the other hand,when the diarylethene converts to the closed-ring form,energy transfer from the donor to the acceptor diarylethene closed-ring form takes place,and the ﬂuorescence is quenched.The quenching efﬁciency is dependent on the distance (or the intermolecular chain length)between the donor and the acceptor chromophores.The FRET systems can be used as nanoscale rulers.The energy transfer is also used to control the electron transfer between porphyrin and fullerene in diarylethene–porphyrin–fullerene triad 15(Scheme 16)[30].Neither the triad open-ring isomer 15a nor the closed-ring isomer 15b showed ﬂuorescence.The model diarylethene–porphyrin dyad compound showed ﬂuorescence from the porphyrin174K.Matsuda,M.Irie /Journal of Photochemistry and Photobiology C:Photochemistry Reviews 5(2004)169–182Scheme 11.when the diarylethene was in the open-ring form.In the closed-ring form,the ﬂuorescence was quenched by the en-ergy transfer from porphyrin to the closed-ring form.In the triad open-ring form (15a ),the photoinduced electron trans-fer from porphyrin to fullerene took place,but the energy transfer prohibited the electron transfer in the closed-ring form (15b ).An anthracene–diarylethene–pyridinium triad 16a was studied in terms of photoinduced electron transfer by Port and co-workers (Scheme 17)[31].The open-ring isomer showed ﬂuorescence with vibrational structures characteristic of an-thracene.The transient spectral measurement showed the ap-pearance of the absorption of the anthracene radical cation,suggesting a photoinduced electron transfer.On the other hand,the closed-ring isomer showed neither ﬂuorescence nor the anthracene radical cation absorption band.The quenching by the closed-ring isomer is considered to affect the electrontransfer.2.4.Photochromism at the single-molecule levelPhotochromic compounds have the feature that the perfor-mance can be detected at a single-molecule level.If a single molecule works as one bit of memory,the ultimate in high-density optical memory can be realized.As a ﬁrst step to this end,photoswitching of the ﬂuorescence of photochromic molecules was followed at the single-molecule level by ir-radiation with UV and visible light [32].Photoswitching of a single molecule has not yet been observed,since con-ventional photochromic molecules readily decompose under high power laser light.The molecule used in this experi-ment was diarylethene 17,in which a highly fatigue-resistant diarylethene and a ﬂuorescent bis(phenylethynyl)anthracene are connected with an adamantane spacer (Scheme 18).When the diarylethene moiety is in the open-ring isomer state,the bis(phenylethynyl)anthracene moiety emits strong ﬂuores-cence,with a ﬂuorescence quantum yield of 0.73.UponK.Matsuda,M.Irie /Journal of Photochemistry and Photobiology C:Photochemistry Reviews 5(2004)169–182175Scheme 13.irradiation with UV light,the diarylethene moiety under-goes a cyclization reaction to give the closed-ring isomer.In the closed-ring isomer state,the ﬂuorescence is quenched to a ﬂuorescence quantum yield of less than 0.001.In the ensemble toluene solution,the ﬂuorescence intensity grad-ually changed upon irradiation with UV or visible light.The analogue-type photoresponse in the ensemble system changed to the digital one at the single-molecule level.Fig.1shows the ﬂuorescence image and digital switching behavior of single molecules embedded in a polymer ﬁlm revealed by confocal microscopy.Initially,a ﬁlm containingnon-Scheme 15.ﬂuorescent 17b molecules was dark,but when irradiated with visible light for 10s,four molecules switched to the ﬂuo-rescent “ON”state.Upon irradiation with weak ultraviolet light for 3s,the ﬂuorescent molecules switched to the non-ﬂuorescent “OFF”state.This digital reversible switching is due to the photochromic reactions.The time trace of the pho-toresponse of a single molecule is shown in Fig.1(b).Start-ing in the “OFF”state,the non-ﬂuorescent molecule abruptly switched to the ﬂuorescent state due to photochromism from176K.Matsuda,M.Irie /Journal of Photochemistry and Photobiology C:Photochemistry Reviews 5(2004)169–182Scheme16.Scheme 17.17b to 17a .The ﬂuorescent molecule switched to the non-ﬂuorescent state as a result of photochromism from 17a to 17b .The ﬂuorescent diarylethene may ﬁnd application in the design of erasable media for ultrahigh-density optical data storage.3.Photoswitching of electrical conductivityIn conductive molecular wires,electrons are delocalized in the ␲-system.If the ␲-conjugated length or ␲-overlaps between adjacent molecules are controlled,electrical con-duction can be modulated.The idea to control the electri-cal conductivity using photochromic compounds was ﬁrst illustrated by Lehn and co-workers [33,34].They used di-arylethene 18a (Scheme 19).The open-ring isomer 18a is quantitatively converted to the closed-ring isomer 18b by ir-radiation with 365nm light,and the closed-ring isomer 18b with visible light (λ>600nm).The cyclic voltammogram of the open-ring isomer 18a showed a reductive wave at −1.04V (versus SCE),but the closed-ring isomer 18b underwent a re-duction process at −0.23V (versus SCE).The conjugation between the two positively charged moieties in the closed-ring isomer 18b decreased the reduction potential to a much less negative value.Diarylethenes are incorporated in the main chain of the conductive polymer 19(Scheme 20)[35].The colorless open-ring isomer 19a converted to the colored closed-ring isomer 19b ,which has an absorption maximum at 560nm,by irradiation with 313nm light.The conversion ratio from the open-to the closed-ring isomers in THF was 35%.While the electrical conductivity of a ﬁlm of the open-ring isomer 19a was 5.3×10−13S cm −1,in the photostationary state the con-ductivity increased to 1.2×10−12S cm −1.The closed-ring isomer is more conductive.The change in the ␲-conjugationK.Matsuda,M.Irie /Journal of Photochemistry and Photobiology C:Photochemistry Reviews 5(2004)169–182177Scheme 18.4.Photoswitching of magnetism 4.1.Intramolecular magnetic interaction in diarylethenesThere is an important characteristic feature in the elec-tronic structure changes of diarylethenes with regard to mag-netic interactions [36].Fig.2shows the open-ring isomer 20a and the closed-ring isomer 20b of radical-substituted diarylethenes with simpliﬁed structures.While there is no resonant closed-shell structure for 20a ,there exists 20b as a resonant quinoid-type closed-shell structure for 20b .While the open-ring isomer 20a exists as a non-Kekul´e biradical,theclosed-ring isomer 20b exists as a normal Kekul´e molecule.The calculated shapes of the two SOMOs of 20a are separated in the molecule and there is no overlap [37].This conﬁgura-tion is a typical disjoint biradical,in which the intramolecular radical–radical interaction is weak [38,39].In the open-ring isomer,the bond alternation is discontinued at the 3-position of the thiophene rings.This is the origin of the disjoint na-ture of the electronic conﬁguration of 20a .In the case of the closed-ring isomer 20b ,the ground electronic state has no unpaired electrons.In this singlet ground state,the magnetic interaction is strongly antiferromagnetic.The electronic structure change of radical-substituted di-arylethenes accompanying the photochromism is thetrans-Fig.1.(a)Fluorescence images and (b)time traces of single ﬂuorescence-photoswitching molecules.formation of a disjoint non-Kekul´e structure to a closed-shell Kekul´e structure.It is inferred from the above consideration that the interaction between spins in the open-ring isomer of the diarylethene is weak,while signiﬁcant antiferromagnetic interaction takes place in the closed-ring isomer.In other words,the open-ring isomer is in an “OFF”state,and the closed-ring isomer is in an “ON”state.4.2.Photoswitching of magnetism using a diarylethene Two radicals are introduced to a diarylethene,as shown in 21(Scheme 21),in which 1,2-bis(2-methyl-1-benzothiophen-3-yl)perﬂuorocyclopentene is employed as a178K.Matsuda,M.Irie /Journal of Photochemistry and Photobiology C:Photochemistry Reviews 5(2004)169–182Scheme20.Scheme21.Fig.2.The open-ring isomer 20a and the closed-ring isomer 20b of the radical-substituted diarylethene.photochromic spin coupler and nitronyl nitroxides as spin sources [37,40].In solution,21a showed ideal photochromic behavior by irradiation with UV and visible light.Although the radical moiety absorbs in the region from 550to 700nm,it did not prohibit the photochromic reaction.Magnetic susceptibilities of 21a and 21b were mea-sured on a SQUID susceptometer in microcrystalline form.χT –T plots are shown in Fig.3.The data were analyzed in terms of a modiﬁed singlet–triplet two-spin model (the Bleaney–Bowers-type)in which two spins (S =1/2)cou-ple antiferromagnetically within a biradical molecule by ex-change interaction J .The best-ﬁt parameters,obtained by means of a least-squares method,were 2J /k B =−2.2±0.04K for 21a and 2J /k B =−11.6±0.4K for 21b .Although the in-Fig.3.Temperature dependence of the magnetic susceptibility of 21a ( )and 21b ( )(χT –T plot).ring isomer 21a is small,the spins of 21b have a remarkable antiferromagnetic interaction (2J /k B =−11.6K).The open-ring isomer 21a had a twisted molecular struc-ture and a disjoint electronic conﬁguration.On the other hand,the closed-ring isomer 21b had a planar molecular struc-ture and a non-disjoint electronic conﬁguration.The photoin-duced change in magnetism agrees well with the prediction that the open-ring isomer has an “OFF”state and the closed-ring isomer has an “ON”state.Although the switching of the exchange interaction was detected by a susceptibility measurement of biradical 21,both the open-and closed-ring isomers 21a and 21b had nine-line ESR spectra,which means that the exchange interaction be-tween the two radicals was much stronger than the hyperﬁne coupling constant in both isomers.To detect the change of the exchange interaction by ESR spectroscopy,the value of the interaction should be comparable to the hyperﬁne coupling constant.To decrease the exchange interaction biradicals 22(n =1,2),in which p -phenylene spacers were incorporated,Scheme 22.Nitronyl nitroxides themselves have two identical nitro-gen atoms to give ﬁve-line ESR spectra with relative in-tensities 1:2:3:2:1and a 7.5G spacing.When two nitronyl nitroxides are magnetically coupled via an exchange inter-action,the biradical gives a nine-line ESR spectrum with relative intensities 1:4:10:16:19:16:10:4:1and a 3.7G spac-ing.If the exchange interaction is smaller than the hyperﬁne coupling in the biradical,the two nitroxide radicals are mag-netically independent and give the same spectrum as the inde-pendent monoradical.In intermediate situations the spectrum becomes complex.Diarylethenes 22a (n =1,2)underwent reversible pho-tochromic reactions in ethyl acetate solution by alternative ir-radiation with 313nm UV light and 578nm visible light.The changes in the ESR spectra accompanying the photochromic reaction were examined for diarylethenes 22a (n =1,2).Fig.4shows the ESR spectra at different stages of the photochromic reaction of 22a (n =1).The ESR spectrum of 22a (n =1)showed a complex of 15lines.This suggests that the two spins of the nitronyl nitroxide radicals are coupled by an exchange interaction that is comparable to the hyperﬁne coupling con-stant.Upon irradiation with 366nm light,the spectrum con-verted completely to a nine-line spectrum,corresponding to the closed-ring isomer 22b (n =1).The nine-line spectrum indicates that the exchange interaction between the two spins in 22b (n =1)is much larger than the hyperﬁne couplingconstant.Fig.4.ESR spectral changes for 22a (n =1)along with photochromism (benzene solution,1.1×10−4M):(a)initial;(b)irradiation with 366nm light for 1min;(c)4min;(d)irradiation with >520nm light for 20min;(e)50min.Table 1Magnetic interaction between two nitronyl nitroxide connected by di-arylethene photoswitchesOpen-ring form isomer Closed-ring form isomer ESR line shape |2J /k B |(K)ESR line shape |2J /k B |(K)219Lines2.29Lines 11.622(n =1)15Lines1.2×10−3<3×10−49Lines >0.0422(n =2)5Lines <3×10−4Distorted 9lines 0.01023(n =1)13Lines 5.6×10−3<3×10−49Lines >0.0423(n =2)5Lines<3×10−49Lines>0.04An ESR spectral change was also observed for 22a (n =2).The open-ring isomer 22a (n =2)had a ﬁve-line spectrum,while the closed-ring isomer 22b (n =2)had a distorted nine-line spectrum.Based on the simulation of the ESR spectra,the dependence of the exchange interaction on the ␲-conjugated chain length was estimated and is shown in Table 1.The exchange interaction change in 22a (n =1,2)upon photoir-radiation was more than 30-fold.Oligothiophenes are good candidates for conductive molecular wires.The thiophene-2,5-diyl moiety has been used as a molecular wire unit for energy and electron transfer and serves as a stronger magnetic coupler than p -phenylene.Diarylethenes 23a (n =1,2)having two nitronyl nitroxideScheme23.Fig.5.Photochromic reaction and schematic illustration of diarylethene 24.radicals at both ends of a molecule containing oligothiophene spacers were prepared (Scheme 23)[43,44].Photochromic reactions and an ESR spectral change were also observed for 23a (n =1,2).Table 1lists the exchange interaction between the two diarylethene-bridged nitronyl nitroxide radicals.For all ﬁve biradicals,the closed-ring isomers have stronger interactions than the open-ring iso-mers.The exchange interactions through the oligothiophene spacers were larger than the corresponding biradicals with oligophenylene spacers.The efﬁcient ␲-conjugation in thio-phene spacers resulted in large exchange interactions between the two nitronyl nitroxide radicals.In the case of bithiophene spacers,the exchange interaction difference between open-and closed-ring isomers was estimated to be more than 150-fold.4.3.Photoswitching using an array of diarylethenes When a diarylethene dimer is used as a switching unit [45],there are three kinds of photochromic states:open–open (OO),closed–open (CO),and closed–closed (CC).From the analogy of an electric circuit,it is inferred that the dimer has two switching units in series.The dimer 24,which has 28carbon atoms between two nitronyl nitroxide radicals,was prepared (Fig.5).A p -phenylene spacer was introduced so that the cyclization reaction could occur at both diarylethene moieties.Bond alternation is discontinued at the open-ring form moieties of 24(OO)and 24(CO).As a result,the twospins at both ends of 24(OO)and 24(CO)cannot interact with each other.On the other hand,the ␲-system of 24(CC)is delocalized throughout the molecule,and the exchange interaction between the two radicals is expected to occur.24(OO)underwent a photochromic reaction by alternate irradiation with UV and visible light.Upon irradiation of the ethyl acetate solution of 24(OO)with 313nm light,an absorption at 560nm appeared.The color of the solution changed from pale blue to red-purple,and then to blue-purple.The red spectral shift suggests the formation of 24(CC).The isosbestic point was maintained at an initial stage of irradia-tion,but it later deviated.The blue-purple solution was com-pletely bleached by irradiation with 578nm light.24(CO)and 24(CC)were isolated from the blue-purple solution by HPLC.24(CC)has an absorption maximum at 576nm,which is red-shifted as much as 16nm in comparison with 24(CO).ESR spectra of isolated 24(OO),24(CO),and 24(CC)were measured in benzene at room temperature (Fig.6).The spectra of 24(OO)and 24(CO)are of the ﬁve-line type,sug-gesting that the exchange interaction between the two nitronyl nitroxide radicals is much smaller than the hyperﬁne coupling constant (2J /k B <3×10−3K).However,the spectrum of 24(CC)is a clear nine-line type,indicating that the exchange interaction between the two spins is much larger than the hyperﬁne coupling constant (2J /k B >0.04K).The result indicates that each diarylethene chro-mophore serves as a switching unit to control the magnetic in-teraction.The magnetic interaction between terminal nitronyl。

icemsurf 物体对称操作

ICEM surf Training Move and symmetry
*Move - Mirror A mirrored image of geometry objects will be computed. The current work plane is used as mirror-plane.
ICEM surf Training Move and symmetry
*Move - Scale - each of the three coordinates can be specified different scaling factors and an arbitrary center of rotation.
ICEM surf Training Move and symmetry
ICEM surf Training Move and symmetry
ICEM surf Training Move and symmetry
-Translation and Rotation is active. -If this option is switched on, additionally, the length of the two axes (b) will be used for computing a scaling. In the example, a curve (c) similar to an original curve (a) is created using Scale .
ICEM surf Training Move and symmetry
*Move - Adjust - a transformation can be computed using a specified number of pairs of points. - point clouds, the 3D position of which does not correspond to the existing geometry, can be adjusted in this way. - Exact information on the desired transformation are not needed in this case.

基于镜像对称补偿技术的脱皮机转子结构优化研究

第38卷第6期2021年6月机电工程Vol.38No.6 Journal of Mechanical&Electrical Engineering Jun.2021DOI：10.3969/j.issn.1001-4551.2021.06.017基于镜像对称补偿技术的脱皮机转子结构优化研究*赵知辛1，薛旭东1，薛琳婧2，潘晓阳1，黄鸣远1，李托雷1(1.陕西理工大学机械工程学院，陕西汉中723000；2.陕西铁路工程职业技术学院高铁工程学院，陕西渭南714000)摘要:为解决谷物脱皮机转子径向膨胀变形的瓶颈问题，根据转子的实际尺寸，建立了转子的有限元模型，对转子的受载特性进行了研究，并对纵梁的变形分布数据进行了拟合°首先，采用两步式策略优化方法及镜像对称方法对模型进行了结构补偿，对转子所受离心载荷进行了计算,确定了p：的取值范围，同时确定了其安全系数及许用应力范围;其次，确定了纵梁扫掠路径的描述函数，采用灵敏度分析方法对参数进行了筛选，采用中心复合设计方法生成了样本;最终得到了3个候选点，对优化结果进行了分析，结果表明：当p：-1.0990mm,p4-3.3011mm,p5—4.5004mm,p6—3.6038mm,p7-2.7477mm,p8-2.1978mm时，纵梁平直度最好，安全系数最高;经补偿，脱皮机转子结构的最大应力降低了12.89%;其最大变形量降低了11.31%；&r值下降了64.30%；安全系数提升了14.78%°研究结果表明:采用镜像对称补偿技术解决脱皮机转子的径向膨胀变形的方法是可行的°关键词:脱皮机转子;有限元法;两步式策略;镜像对称方法；中心复合设计中图分类号:TH69汀H122；S226.4文献标识码：A文章编号：1001-4551(2021)06-0774-07Rotor structure optimization of peeling machine based on mirrorsymmetry compensation technologyZHAO Zhi-xin：,XUE Xu-dong：,XUE Lin-jing2,PAN Xiao-yang：,HUANG Ming-yuan：,LI Tuo-lei：(1.Department of Mechanical Engineering,Shaanxi University of Technology,Hanzhong723000,China;2.School of High-Speed Railway Engineering,Shaanxi Railway Institute,Weinan714000,China)Abstract:In order to solve the bottleneck problem of radial expansion deformation of the rotor of grain peeling machine,the finite element model of the rotor was established according to the actual size of the rotor,the load characteristics of the rotor were studied,and the defor^na-tion distribution data of the longitudinal beam were fitted.First,two-step strategy optimization method and mirror symmetry method were used to compensate the structure of the model:the centrifugal load of the rotor was calculated,the range of p；,the safety factor and allowable stress range was determined.Then，the description function of longitudinal beam sweeping path was determine.Finally，the sensitivity analysis method was used to screen the parameters，and the central composite design method(CCD)was used to generate samples.The results shows that when p：-1.0990mm,P4-3.3011mm,p5-4.5004mm,p§-3.6038mm,p7-2.7477mm,p&-2.1978mm,the longitudinal beam has the best flatness and the highest safety factor.After compensation，the maximum stress of the rotor structure is reduced by 12.89%,the maximum deformation is reduced by11.31%,the S£r value has reduced by64.30%,and the safety factor is increased by 14.78%.The mirror symmetry compensation technology is effective and feasible for solving the radial expansion deformation of the rotor of the peeling machine.Key words:rotor of peeling machine；finite element method；two-step strategy；mirror symmetry；central composite design(CCD)收稿日期：2020-：0-：8基金项目：陕西省科技厅重点研发计划项目(20I9GY-068)；陕西省教育厅专项科研计划项目(16JK147)作者简介：赵知辛(1973-)，男，陕西西安人，博士，讲师，主要从事机械优化设计方面的研究°E-mail：49989803@第6期赵知辛,等:基于镜像对称补偿技术的脱皮机转子结构优化研究•775•0引言以FBPY型脱皮机为基础,某企业进一步研发出了FBGY型双筒式谷物脱皮机。

光子晶体课件

下面是两能带各自的concentration factor
A Square Lattice of Dielectric Veins
X点的集中参数
TM模式的band1把能量集中在vein的交叉点，TE模式把能量集中在vein 的交叉点之间连线上，能量都集中在高介电常数区域，所以不会出现 gap。而对于TE模式，band1电场线集中在穿过交叉点的vein上，而 band2必须穿入空气，所以出现gap。
Electromagnetism
Symmetry
1D PhC (Layer)
2D PhC (Slab)
3D PhC
macroscopic Maxwell equations
Constitutive relations
ρ = 0 and J = 0; ignorable nonlinearity
Electromagnetism
The photonic band structures for on-axis propagation
The low frequency modes concentrate their energy in the high-ε regions, and the h-igh frequency modes have a larger fraction of their energy in the low-ε regions.
Off-Axis Propagation
1.离轴方向上没有明显的禁带
与on-axis传播相比的区别 2.原on-axis传播的旋转对称性不存在了存在旋转对称性的时候TE模、TM模是简并的，虽然离轴时旋转对称性不存在了，但有可能存在其他对称性，如镜面对称性等

Aesthetics of Symmetry

Aesthetics of Symmetry
Aesthetics
Aesthetics comes from the Greek word aisthetike; coined by the philosopher Alexander Gottlieb Baumgarten to mean “The science of how things are known via the senses.”
Aesthetics is defined by the Oxford English Dictionary as : 1. Concerned with beauty or the appreciation of beauty 2. Set of principles of good taste and the appreciation of beauty
Symmetry is defined by the Oxford English Dictionary as :
1. Correct or beautiful proportion of parts; balance; harmony. 2. Repitition of exactly similar parts facing each other or a center.
Types of Symmetry
There are many types of symmetry such as Directional, Rotoreflectional, Glide rቤተ መጻሕፍቲ ባይዱflectional, Helical, Scale symmetry and fractals. The most common types are reflection (bilateral or mirror symmetry), rotation, and translation. These symmetries may also be found in combinations of each other. We’ll be looking at examples of mirror symmetry, rotation, translation, and Helical.

Robust Real-Time Periodic Motion Detection

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,
VOL. 22, NO. 8,
AUGUST 2000
781
Robust Real-Time Periodic Motion Detection, Analysis, and Applications
~ t p ~ t ~ tY I ~ t is a translation of the point. The period p is the where smallest p b H that satisfies (1); the frequency of the motion is Iap. If p is not constant, then the motion is cyclic. In this work, we analyze locally (in time) periodic motion, which approximates many natural forms of cyclic motion. Periodic motion can also be defined in terms of symmetry. Informally, spatial symmetry is self-similarity under a class of transformations, usually the group of Euclidean transformations in the plane (translations, rotations, and reflections) [36]. Periodic motion has a temporal (and sometimes spatial) symmetry. For example, Figs. 3a, 4a, 5a, and 6a show four simple dynamic systems (pendulums). For each system, the ~ t p ~ t for a point ~ t on the motion is such that pendulum. However, each system exhibits qualitatively different types of periodic motion. Fig. 5a is a simple planar pendulum with a fixed rod under a gravitational field. The motion of this system gives it a temporal mirror symmetry along the shown vertical axis. The system in Fig. 4a is a similar pendulum, but with sufficient initial velocity such that it always travels in one angular direction. The motion of this system gives it a temporal mirror symmetry along the shown vertical axis. The system in Fig. 3a is a similar pendulum, but in zero gravity; note it has an infinite number of axes of symmetry that pass through the pivot of the pendulum. The system in Fig. 6a consists of a pair of uncoupled and IVH out of phase pendulums, a system which is often used to model the upper leg motion of humans [24]. This system has a temporal mirror symmetry along the shown vertical axis, as well as an approximate spatial mirror symmetry along the

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