晶体缺陷的TEM图象TEM imaging of crystal defects.pdf

Defects in TEMR.SchublinChapter 11TEM imaging of crystal defectsRobin SchublinCRPP-EPFLrobin.schaeublinpsi.chDefects in TEMR.Schublin1.Introduction?1.1 Motivation2.Defects in TEM?2.1 Origin of contrast?2.2 g.b analysis?2.3 Weak-beam technique3.Transmission Electron Microscopy imaging?3.1 Image simulations?3.1.1 TEM imaging of defects?3.1.2 Simulation techniques(many beam,multislice)?3.2 Applications?3.2.1 Dislocation splitting?3.2.2 Dislocation loops?3.2.3 Stacking fault tetrahedra4.Positron Annihilation Spectroscopy5.Small Angle Neutron ScatteringDefects in TEMR.SchublinIntroductionDefects in crystals influence their physical and chemical properties properties.Examples:Electrical behaviour of semiconductors(loss of dopants at defects,.)Mechanical properties of metals and alloys(hardening,loss of ductility,.)Without dislocations crystals would not plastically deform,but break like glass.Thus the importance to identify and characterize crystal defectsDefects in TEMR.SchublinThe dislocationDislocation is described mathematically by its displacement field using e.g.linear anisotropic elasticity of the continuum(Stroh 1958),allowing for any type(edge,screw,mixed).Defects in TEMR.SchublinITER(International Thermonuclear Experimental Reactor)Operational in 2020Q?10Fusion power:500 MWCost:5 billion US$Promises of the fusion reactor:Long term,sustainable andeconomic energy source.Safe(no risk of a nuclearaccident as for fission reactors).Minimal long lived radioactiveproducts.Possible recycling of structuralmaterials,lithium coolant,unburnedor burned fuel.Defects in TEMR.Schublinatome de la cible interstitiellacuneimpuretlgende:The displacement cascadeProduction of:Interstitials Vacancies Impurities Clusters of interstitials,vacancies and impuritiesDefects in TEMR.SchublinIrradiation leads to:Hardening and loss of ductility,by the structural defects formed by the residues of displacement cascades Swelling,by the formation of bubbles of gas resulting from transmutation Activation,though limited,by the formation of radioisotopes by transmutationTensile test of single crystal NiTensile test of F/M steel F82HDefects in TEMR.SchublinSingle crystal pure Ni,unirradiatedDeformed in uniaxial tension at 5x10-5 s-1Traction axis:Test duration:3.5 hours,elongation:120%Effect on the plasticityDefects in TEMR.SchublinSingle crystal pure Ni,irradiated to 0.1 dpa at room temperatureDeformed in uniaxial tension at 1x10-4 s-1Traction axis:Test duration:2 hours,elongation:120%Defects in TEMR.Schublin100 nm25 nm10 nmResulting microstructure:Defects in TEMR.SchublinDeformation proceeds by flow localization or defect free channelsChannels appearing in deformed irradiated single crystal pure NiChannel crossing a grain boundary in irradiated polycristalline Fe-12CrDefects in TEMR.SchublinHardening:?=?b Nd1/2Need for accuracy in the determination of:Defect density(N)Defect size(d)Obstacle strength(?)Works in pure fcc metalsDoes not work in bcc Fe and F/M steelsDifficulty in TEM resides in the size of the radiation induceddamage that is at the limit of the TEM resolution(about 1 nm).-Need for good TEM observations and image matching to simulationsDefects in TEMR.SchublinFe edge dislocation 2 nm void 10 KDefects in TEMR.Schublinfcc Cu,irradiated,deformed in-situ,TV cameraDefects in TEMR.Schublinfcc Cu,irradiated,deformed in-situ,CCD cameraDefects in TEMR.Schublinfcc Cu,irradiated,deformed in-situ at 183 K,CCD camera“The string”Defects in TEMR.SchublinThe Utterly Butterly aerobatic team perform at the Zhuhai Airshow 2004 in southern China.US pair,Melissa Gregory and Denis Petukhov,perform during theIce Dance 2004 original dance in Nagoya,Japan.Image interpretation problem.TEM and material defectsExperimentsSimulationsCu 0.01 dpa RTweak beam g(6g)g=(200)Molecular dynamics simulationPair potential method,100000 atomse.g.Stacking fault tetrahedra in irradiated copperModelisation2 nm50 nm?Defects in TEMR.Schublin1.Introduction?1.1 Motivation2.Defects in TEM?2.1 Origin of contrast?2.2 g.b analysis?2.3 Weak-beam technique3.Transmission Electron Microscopy imaging?3.1 Image simulations?3.1.1 TEM imaging of defects?3.1.2 Simulation techniques(many beam,multislice)?3.2 Applications?3.2.1 Dislocation splitting?3.2.2 Dislocation loops?3.2.3 Stacking fault tetrahedra4.Positron Annihilation Spectroscopy5.Small Angle Neutron ScatteringDefects in TEMR.Schublin Objective lensObjective lensSampleSampleObjective apertureObjective apertureFilmFilmDiffraction contrastDiffraction contrastimaging modeimaging modeHigh ResolutionHigh Resolutionimaging modeimaging mode37-interstitial Frank37-interstitial Frankloop in Alloop in Al2 nmElectrons?1.1 MotivationDefects in TEMR.Schublinbeam direction:?+g+SgSg-g0g2g3g4g5g?0?1?4Sg:deviation parameterEwald spheresystematic rowCrystal and the beams in the reciprocal space.?is the direction of the transmitted beam,g is the reciprocal lattice vector and sg the deviation parameter.(?+g+sg)is the direction of the beam with index g.Ewald constructionDefects in TEMR.SchublinDiffraction conditionDefects in TEMR.SchublinDefects in TEMDistortedcrystalPerfectcrystalDislocation incrystalIntensity profileReal positionImage position?Dislocation Burgers vector?g.b analysisDislocation image position?Defect sizing,dissociation width,natureDefects in TEMR.Schubling.b analysisg perpendicular to b dislocation invisible,g.b=0b 3 unknowns 3 equationsIn practice:Minimum 4 different g,non-coplanarEdge component give residual contrastComplete extinction only when g.b x u=0Best g?Sharp,thin dislocation contrastDefects in TEMR.Schublin(200)(01-1)(21-1)(200)(020)(110)001113112223111233123011023012013133122(01-1)(1-10)(10-1)(1-10)(22-2)(1-10)(21-1)(12-1)(-200)(12-1)(-12-1)(-200)(03-1)555BCC crystal orientation mapDefects in TEMR.SchublinFCC crystal orientation map001113112223111233123011023012013133122(2-20)(2-20)(11-1)(-200)(04-2)(-200)(13-1)(-13-1)555(200)(020)(220)(200)(11-1)(-11-1)(02-2)(20-2)(2-20)(42-2)(24-2)Defects in TEMR.SchublinHCP crystalorientation map2-1-105-1-4010-107-2-532-1-114-2-232-1-122-1-1310-1110-1210-1210-1300012-1-192-1-162-1-164-2-29 4 index 3 indexDirection:u,v,t,w U,V,WPlane:(h,k,i,l)(H,K,L)From 4 to 3:From 4 to 3:U=u-tH=hV=v-tK=kW=wL=lh+k=-i and u+v=-tFrom 3 to 4:From 3 to 4:u=2/3*U-1/3*Vh=Hv=2/3*V-1/3*Uk=Kt=-1/3*V-1/3*Ui=-(H+K)w=Wl=L000-21-210000-20-110000-21-3200-1101-2100-1102-1-1-11-10-30-1100-1100-1101-10-11-10-22-1-1010-105-1-4610101-1001-21010-1-11-2101-10-10-11110-1-210-1-210-1-11-21-21-21-22-20-12-20-10-111Defects in TEMR.SchublinDislocation densityUnit of m-2Number of intersections N with dislocations made by random straight lines of length LDensity=2 N/L t (t:foil thickness)Problems:Dislocations lost during sample preparationOverlapping of dislocationsFor a given family of dislocation(same type of b,e.g.1/2110)some can be invisible:hklProportion of invisible disloc.1111/22001/32201/63111/62221/24001/33311/6420all visibleDefects in TEMR.SchublinContrast of a dislocation loopInterstitial or vacancy nature of the loop?Inside-outside contrast analysis Defects in TEMR.SchublinContrast of a dislocation loopAnalysis depends on size d of the loop:d 50 nm same as for dislocations10 nm d 50 nm Inside/outside contrast analyis(coffee bean contrast)d 0.2 nm-1 ensures a single image per dislocation or partial dislocationImage position of dislocation is given by:The“turning point”Dislocation contrast width:Defects in TEMR.Schublin1.Introduction?1.1 Motivation2.Defects in TEM?2.1 Origin of contrast?2.2 g.b analysis?2.3 Weak-beam technique3.Transmission Electron Microscopy imaging?3.1 Image simulations?3.1.1 TEM imaging of defects?3.1.2 Simulation techniques(many beam,multislice)?3.2 Applications?3.2.1 Dislocation splitting?3.2.2 Dislocation loops?3.2.3 Stacking fault tetrahedra4Positron Annihilation Spectroscopy5.Small Angle Neutron ScatteringDefects in TEMR.SchublinTEM image simulationsEvery image detail,or contrast,appearing on the phosphorescent screen of a transmission electron microscope(TEM)is the result of the interaction of the electron beam with the sample.Unlike the direct interpretation we can give of the eye visible world,the interpretation of TEM micrographs is far from straightforward and has to be considered carefully.The origins of the TEM contrasts are complex and multiple.They are divided here into the following four categories:?Absorption contrastStructure contrast,?Diffraction contrast,?Phase contrast.The contrast formation theories,eventhough based on sometimes tricky approximations,give a good description of the TEM images.With the help of these theories,the TEM images can be reproduced by large numerical calculations.The image simulation appears as a powerful tool for the identification of an object at the origin of an observed contrast.First question:What contrast is the most appropriate in looking at small 3D crystal defects?Defects in TEMR.Schublin Objective lensObjective lensSampleSampleObjective apertureObjective apertureFilmFilmDiffraction contrastDiffraction contrastimaging modeimaging modeHigh ResolutionHigh Resolutionimaging modeimaging mode37-interstitial Frank37-interstitial Frankloop in Alloop in Al2 nmElectronsDefects in TEMR.Schublinbeam direction:?+g+SgSg-g0g2g3g4g5g?0?1?4Sg:deviation parameterEwald spheresystematic rowCrystal and the beams in the reciprocal space.?is the direction of the transmitted beam,g is the reciprocal lattice vector and sg the deviation parameter.(?+g+sg)is the direction of the beam with index g.Defects in TEMR.SchublinTEM image simulationsThere are two main types of simulation techniques:1)Many beam calculation2)Multislice calculationThe many beam calculation originates from the calculation of intensities of X-Ray diffraction(1930s).The idea is to integrate the various beams seen in diffraction along a thin column going trough the specimen.At the end of the integration one gets the intensity of the pixel beneath the column.In TEM it is well known for the case of two beams,the transmitted and one diffracted beam.They form the equations of Howie and Whelan.While they work fine for most of the cases in CTEM,i.e.imaging performed in bright field and dark field,where 90%of the intensity in concentrated in these two beams,it does not hold true anymore for dark field weak beam(or in kinematical condition),which is needed for higher contrast and higher spatial resolution.Thus the need for many beam calculation.It takes into account:1)the displacement field of the defect configuration and2)the diffraction condition.The multislice technique originates from the first calculations of high resolution atomic images of perfect crystal structures by Cowley and Moodie(1957).The idea is to propagate an incident planar electron wave through thin slices composing the specimen,slice after slice.It takes into account:1)the atomic positions in the sample.Defects in TEMR.SchublinA summary of the theory of electron propagation in thin crystals is given here,as it will help to understand beam contribution in the many beam calculation.To calculate the propagation of electrons in a faulted crystal,we use the dynamical theory of contrast(see Hirsch et al.Hirsch,1969).The crystal at a point r is described by a faulted potential V(r)that can be written as a Fourier serie:The summation is done over all reciprocal lattice vectors g,with me the electron mass and h the Planck constant.R(r)describes the displacement field around the lattice defect.The Schrdingers wave equation is:?(r)is the function associated to the electron wave that moves through the faulted crystal.The proposed solution to the Schrdinger equation is:The?g(r)function are associated with the beams that come out of the sample,including the transmitted beam(beam 0)and the diffracted beams(beam 1 to n).The contrast intensity I recorded on the micrographs for a g image,is simply I=?g(r)?g(r).V(r)=h22 me Ug exp(-2?i gR(r)exp(2?igr)?g?2?(r)+(8?2meh2)E+V(r)?(r)=0?(r)=?g exp(2?i(?+g+sg)r)?gMany beam calculation-Howie-Whelan equations for two beamsDefects in TEMR.SchublinWe will take a co-ordinate?g along every beam direction.We then substitute V(r)and?(r)in the Schrdinger equation.We obtain a system of n differential equations of the first order with n unknowns?g(r):The equations are to be integrated along the proper beam direction?g.This is difficult to solve analytically.To simplify,we use the column approximation that allows to make the integration along the same direction for all beams.Column approximationThe column approximation means that we consider only the direction of the transmitted beam to make the integration;so that:?g(r)?g?i?g-h?h?h(r)exp(2?i(h-g)R(r)+2?i(sh-sg)r)?g?ddzMany beam calculationDefects in TEMR.SchublinWe can then write the equation system in a matrix form:The matrix M is symmetrical and has the following expression:d?(r)dz=M?(r)where:?(r)=?0?1?nAA1.Ai.AnA1B1 Cij Ai Bi Cij An BnMany beam calculationDefects in TEMR.SchublinWhere the coefficients are:?i is the extinction distance which becomes large if the beam i gets far from the transmitted beam;?i is proportional to?i.?1 is a scaling factor that was originally introduced by Head et al.to avoid convergence problems and save calculation time in the integrations.A=-?1?0Ai=i?11?i+i?iBi=-?1?0+2isi?1+2?iddzgiR(r)Cij=i?11?i-j+i?i-jMany beam calculationDefects in TEMR.SchublinWe use relation(6)to compute d?o(r)/dz:The general equation for a d?i(r)/dz is:These equations show that the derivative of each beam is a linear combination of all the beams.The contribution of each beam in the linear combination is weighted by the matrix coefficients.The physical meaning of these relations is that the contribution of a beam i depends on the associated deviation parameter si(diffraction condition),the associated extinction distance?i(material characteristics)and a cross-term?i-j that has the expression of an extinction distance.High IiI values correspond to large?i and therefore beam i may have a weak contribution;but when this same beam has a small deviation parameter si,it may have a strong contribution.It appears that the importance of a beam(i)contribution is a balance between si,deduced from the observation conditions and?i,given by the material characteristics.This had to be taken into account in the choice of the beams included in the calculation.The general rule is the following.Beams have to be close to the transmitted beam(small?i)and situated close to the Ewald sphere intersections with the systematic row(small si).d?0dz=-?1?0?0+i?11?i+i?i?i+i?11?n+i?n?nd?kdz=i?11?i+i?i?0+i?11?i-j+i?i-j?j+-?1?0+2i si?1+2?i ddz gi R(r)?i+i?11?i-n+i?i-n?nMany beam calculationDefects in TEMR.SchublinReferencesC.T.Forwood and L.M.Clarebrough,“Electron Microscopy of Interfaces in Metals and Alloys”,Adam Hilger Ed.,Bristol,Philadelphia and New York,1991.A.K.Head,P.Humble,L.M.Clarebrough,A.J.Morton and C.T.Forwood,“Computed Electron Micrographs and Defect Identification”,North-Holland Publishing Company