1、10/7/2022h1第四章第四章 透射电镜透射电镜(TEM)Transmission Electron Microscopy刘炳泗Department of Chemistry Tianjin University10/7/2022h2一、一、Interactions of Electrons with Matter 1.Elastic Interactions No energy is transferred from the electron to the sample(direct beam or is scattered).TEM,SAED2.Inelastic Interactio
2、ns Energy is transferred from the incident electrons to the sample:(EDX analysis)10/7/2022h31.Elastic Interactions An electron penetrating into the electron cloud of an atom is attracted by the positive potential of the nucleus(Coulombic interaction),and its path is deflected towards the core as a r
3、esult.The Coulombic force F is defined as:with r being the distance between the charges Q1 and Q2 and 0 the dielectric constant.The closer the electron comes to the nucleus,i.e.the smaller r,the larger is F and consequently the scattering angle.In rare cases,even complete backscattering can occur(ba
4、ck scattered electrons BSE).20214rQQF10/7/2022h42.Inelastic InteractionsIonization:The high-energy electrons of the incident beam can transfer a critical amount of energy to an inner-shell electron of an atom,leading to the ejection of this electron.The ionization energy is provided by the incident
5、electron,reducing its energy.This leads to an ionization edge in the electron energy loss spectrum(EELS).Subsequently,the hole in the inner-shell is filled up by an electron with higher energy from an outer shell.This electron gives away a part of its energy,leading to the emission of characteristic
6、 X-rays or Auger electrons.Secondary electrons:Electrons in the conduction or valence band do not need much energy(low work function)to be transferred into vacuum.Thus,the energy of secondary electrons(SE)is low(50 eV).The SEs are mainly exploited in SEM.Phonons:Phonons are lattice vibrations,which
7、are equal to heating the specimen.This effect may lead to a damage of the sample.Plasmons:Plasmons are longitudinal oscillations of free electrons,which decay either in photons or phonons.Cathodoluminescence:If semiconductors are hit by high-energy electrons,electron-hole pairs can be formed by prom
8、oting an valence electron into the conduction band.Filling this hole with an electron from the conduction band(recombination)leads to the emission of light with a frequency that corresponds to the band gap.10/7/2022h5Basic contrast mechanisms in TEM and STEM.Electrons,which come from the condenser s
9、ystem of the TEM,are scattered by the sample,situated in the object plane of the objective lens.Electrons scattered in the same direction are focused in the back focal plane,and as a result,a diffraction pattern is formed there.Electrons coming from the same point of the object are focused in the im
10、age plane.In the TEM,the first intermediate image is magnified by further lenses(projective system).10/7/2022h6basic contrast mechanisms in TEM and STEM.Bright field(BF)mode:Mass-thickness and diffraction contrast contribute to image formation:thick areas,areas in which heavy atoms are enriched,and
11、crystalline areas appear with dark contrast.In dark field(DF)images:Since diffracted beams have strongly interacted with the s p e c i m e n,v e r y u s e f u l information is present in DF images,e.g.,about planar defects,stacking faults or particle size.10/7/2022h7BF and DF TEM images of ZrO2 Elec
12、tron diffraction pattern:the spots indicate the presence of single microcrystals.The apertures(red circles)are localized around the direct beam for recording the bright field(BF)image and around a few diffracted beams for the dark field(DF)image.The intense direct beam is blocked by a metal rod(blac
13、k shadow on the left center)to avoid overexposure.BFDF10/7/2022h8HRTEM modeIf the point resolution of t h e m i c r o s c o p e i s sufficiently high and a suitable sample oriented along a zone axis,then(HRTEM)images are obtained.In many cases,the atomic structure of a specimen can directly be inves
14、tigated by HRTEM.10/7/2022h9HRTEM modesingle crystals of(Ce0.5Zr0.5)O2 Ag particle supported on ZnO R e O 3 Structure10/7/2022h10Scanning Electron Microscopy(SEM)compact samples can thus be investigated by SEM.A valuable information about morphology,surface t o p o l o g y a n d composition can be o
15、 b t a i n e d.S E M m i c r o s c o p e s achieving resolutions below 1 nm are available now.10/7/2022h11SEM:Imaging with Back-scattered ElectronsSEM images of Fe particles in carbon recorded with the secondary electron(left)and the back-scattered(right)electron detector.The BSE image shows the Fe
16、particles with bright contrast.10/7/2022h12 二、Imaging and Diffraction 1.objective lens forms a diffraction pattern in the back focal plane 2.diffraction pattern and image are simultaneously present 3.real space(image)to reciprocal space(diffraction pattern)is easily achieved by changing the strength
17、 of the intermediate lens.4.Aperture regulation10/7/2022h13三、Scheme of a CM30 TEMElectron gun:2.Condenser system3.Objective lens 4.Diffraction/inter-mediate lens:5.P ro j e c t i v e lenses:6.I m a g e observation:7.V a c u u m system:10/7/2022h14四、四、Bragg Description of Diffraction If the incident
18、plane wave hits the crystal at an arbitrary angle,the interference of the reflected waves can be either destructive or constructive.Destructive interference of reflected waves(Max.and Min.of the wave amplitude are superimposed).Constructive Interference of reflected waves(maxima are superimposed).10
19、/7/2022h15To obtain constructive interference,the path difference between the two incident and the scattered waves,which is 2dsin,has to be a multiple of the wavelength.For this case,the Bragg law then gives the relation between interplanar distance d and diffraction angle:sin2dn 10/7/2022h16Electro
20、n Diffraction(ED)Electron diffraction is a collective elastic scattering phenomenon with electrons being scattering by atoms in a regular array(crystal).The incoming plane electron wave interact with the atoms.Secondary waves are generated which interfere with each other.This occurs either construct
21、ively(reinforcement)or destructively(extinguishing).As in X-ray diffraction(XRD),the scattering event can be described as a reflection of the beams at planes of atoms(lattice planes).The Bragg law gives the relation between interplanar distance d and diffraction angle:sin2dn 10/7/2022h17Since the wa
22、velength of the electrons is known,interplanar distances can be calculated from ED patterns.Furthermore,information about crystal symmetry can be obtained.Consequently,electron diffraction represents a valuable tool in crystallography.sin2dn 10/7/2022h18Estimate of scattering anglesel=0.00197 nm(1.9
23、7 pm)for 300 kV electrons.A typical value for the interplanar distance is d=0.2 nm.If these values are put in the Bragg law,then the scattering angle is:=0.28.As a rule,the scattering angles in ED are very small:0 2.sin2dn 10/7/2022h191.Reflecting lattice planes are almost parallel to the direct bea
24、m.2.Incident electron beam is the zone axis of the reflecting sets of lattice planes 10/7/2022h20Comparison of Electron(ED)and XRD Both,ED and XRD,are caused by positive interference of scattered waves,and the same fundamental laws(e.g.,Bragg law,extinction rules)can be applied for the interpretatio
25、n of the resulting diffraction patterns.In both cases,diffraction patterns of powders and of single crystals appear.However,ED shows some unique characteristics:10/7/2022h211.The wavelength of electrons(e.g.,1.97 pm for 300 keV electrons)is much shorter than that of X-rays(about 100 pm).Therefore,th
26、e radius of the Ewald sphere is much larger and more reflections arise.2.The diffraction angles are very small:ED 0-2(cf.,XRD 0-180)3.Electrons are scattered by the positive potential inside the electron cloud,while X-rays interact with the electron cloud.As the result,the interaction of electrons w
27、ith matter is much(106-107)stronger than that of X-rays.10/7/2022h22The advantage and the disadvantage of EDthe diffracted electron beams have a high intensity and exposure times.ED patterns can directly be observed on viewing screen of TEM.diffraction patterns can be obtained from very small crysta
28、ls selected with a diffracted aperture(Selected Area Electron Diffraction SAED)1.m u l t i p l e scattering plays an important role,T h i s m a k e s s t r u c t u r e determination from ED more difficult and less reliable than that from XRD data.10/7/2022h23Ewald Sphere of Diffraction The diffracti
29、on,which mathematically corresponds to a Fourier transform,results in spots(reflections)at well-defined positions.Each set of parallel lattice planes is represented by spots（distance of 1/d：d:interplanar spacing)from the origin and which are perpendicular to the reflecting set of lattice plane.10/7/
30、2022h24La2NiO4(4 cm/2 cm)*5 1/nm=(10 1/nm)=(1/10 nm)=0.1 nmCatal.Today,131(2008):53310/7/2022h25C a r b o n deposition over Mo2C/ZSM-510/7/2022h26Calculation:(0.81 cm/2 cm)*5 1/nm=(2.025 1/nm)=0.494 nm1/d=0.493 nm1/d=0.294 nmSAED of Mo2CUnit Cell:Hexagonala=0.3002 nmb=0.4724 nmAIChE J 57(2011):18521
31、0/7/2022h27The diffraction can be described in reciprocal space by the Ewald sphere construction(Figure below).A sphere with radius 1/is drawn through the origin of the reciprocal lattice.Now,for each reciprocal lattice point that is located on the Ewald sphere of reflection,the Bragg condition is s
32、atisfied and diffraction arises.10/7/2022h28point 0:origin of reciprocal latticek0:wave vector of the incident wavekD:wave vector of a diffracted waveZOLZ:Zero Order Laue ZoneFOLZ(SOLZ):First(Second)Order Laue Zone 10/7/2022h29Due to the small wavelength of electrons(e.g.,=1.97 pm for 300 keV electr
33、ons),the radius of the Ewald sphere is larger and many reflections appear.Furthermore,the lattice points are elongated in ED to form rods so that the Ewald sphere intersects more points(see figure).Because of that,diffraction occurs even then the Bragg condition is not exactly satisfied.In fact,ED p
34、atterns are 2D cuttings of reciprocal lattice.The rod-shape is due to the fact that TEM specimens are very thin in real space,leading to an elongation in reciprocal space.If the interplanar distance in direction of observation is large(that means a small distance between ZOLZ and FOLZ in reciprocal
35、space),higher order Laue zones(HOLZ)can be observed as well.A general introduction into diffraction is given in an interactive tutorial by Proven and Neder.10/7/2022h30Electron diffraction patterns of Ta97Te60 along two perpendicular directions.The parameters of the tetragonal unit cell can be deter
36、mined from these SAED patterns:a=27.6,c=20.6.10/7/2022h31Electron diffraction pattern of YbSi1.41 along 001.The reflection condition:h+k=2n for hkl(C face centering)is fulfilled.10/7/2022h32E D p a t t e r n o f p o l y c r y s t a l l i n e platinum.The indices are assigned to the diffraction rings
37、 in accordance of the face-centered cubic l a t t i c e o f P t(reflection condition:h,k,l all even or all odd).10/7/2022h33In the pseudo-binary system Nb2O5/WO3,Nb8W9O47,crystallizing in a threefold superstructure of the tetragonal tungsten bronze(TTB)type,represents the most stable compound.The su
38、perstructure arises from a systematic occupation of a part of the pentagonal channels with metal-oxygen strings(see figure).HRTEM image of Nb4W1 3O4 7 along 001.The insets show the structural model and a simulation(EMS program).10/7/2022h34HRTEM image and SAED(inset)of Al-MCM-41(50).Liu BS et al J P
39、hys Chem.C 2008,112:15490SBA-1510/7/2022h35SBA-1510/7/2022h36STEM+EDXSPoint Analysis in STEMIn STEM,an electron beam is scanned over a defined area of the sample.The beam can be localized on a certain point in the image and used to measure an EDX and/or EEL spectrum at there.Moreover,line scans and
40、mappings can be obtained by this powerful technique.Example:Molybdenum Tungsten Oxide10/7/2022h37To solve the question whether the nanorods consist of a mixed Mo-W oxide or of the separated binary oxides MoO3 and WO3,spot analyses were performed.The EDX spectrum obtained at the position encircled in
41、 the HAADF-STEM image shows both metals and thus proves the presence of a mixed oxide X-ray Spectroscopy X-ray spectroscopy is a valuable tool for qualitative and quantitative element analysis.Each element has characteristic peak positions corresponding to the possible transitions in its electron sh
42、ell.10/7/2022h38The presence of copper,for example,is indicated by two K peaks at about 8.0 and 8.9 keV and a L peak at 0.85 eV.In heavy elements like tungsten,a lot of different transitions are possible and many peaks are therefore present.TEMs are almost exclusively equipped with energy-dispersive
43、 spectrometers(energy-dispersive X-ray spectroscopy EDXS).10/7/2022h39Generation of X-rays 1.Ionization:A hole in an inner shell(here:K shell)is generated by an incident high-energy electron that loses the corresponding energy E transferred to the ejected electron.*2.X-ray emission:The hole in the K
44、 shell is filled by an electron from an outer shell(here:L3).The superfluous energy is emitted as a characteristic X-ray quantum.In a typical X-ray spectrum,there are many peaks caused by such a process.The X-ray energy corresponds to a certain difference in inner-shell energies.Thus,the detection o
45、f characteristic X-ray is specific for a element in the sample,and X-ray spectroscopy can be employed for qualitative analysis.10/7/2022h40Generation of X-rays Another inelastic interaction of the incident electron with matter represents its deceleration by the Coulomb field of the nucleus.This proc
46、ess creates X-ray with any energy smaller than the beam energy.These X-rays are called bremsstrahlung and form the uncharacteristic spectrum background.If the X-ray spectrum was measured on a TEM,the Cliff-Lorimer ratio technique can be applied for the quantification:NA/NB=kAB IA/IBNA,NB:atomic%of e
47、lement A,B.IA/IB:measured intensity of element A,B.kAB:Cliff-Lorimer factor.Quantitative X-rays Analysis10/7/2022h41Generation of X-rays The Cliff-Lorimer factor is NOT a constant but depends on the TEM voltage,on the detector efficiency and several other parameters.Thus,accurate results can only be
48、 obtained if a standard containing the elements A and B in a well-defined ratio is used to determine kAB.Calculated values of kAB,which are given by the various programs used for X-ray spectroscopy,are only raw approximations and can only be used for quick and rather inaccurate analyses.Although the
49、 program output for the composition is a seemingly accurate value with a rather small error bar,the actual error might be much higher because of the kAB problem.In all cases,the background(bremsstrahlung)has to be subtracted first.The accuracy of the quantification is additionally reduced by statist
50、ical errors of the measurement,absorption,fluorescence,and electron channeling,just to mention the most important effects.10/7/2022h42Generation of X-rays 10/7/2022h43 Detector Absorption Element Weight%Atomic%Uncertainty%Correction k-Factor Correction-O(K)25.084 53.382 0.381 0.495 2.059 0.952Si(K)2
