MSE 522 Advanced Transmission Electron Microscopy. Sample preparation

Transcription

1 Sample preparation Preparin samples for use in the TEM is not a trivial exercise. In order to be inserted into the microscope, the sample must be a 3mm-diameter disk thin enouh to be electron-transparent. A. Inoranic samples The most common way of preparin electrically conductive materials like metals is electropolishin or jet polishin. The principle of this method is that the specimen is made the anode in an electrolytic cell. When a small voltae is applied, metal is dissolved from the anode and deposited on the cathode. The thin specimen becomes both thinner and smoother, and eventually a hole appears in the sample. The reions around the hole should be thin enouh for viewin in the TEM. Automated electropolishers produce 3mm disk samples consistin of relatively thick rims supportin the thin central reion. Such samples made in this way are often called foils. Ceramic samples can be prepared in a number of ways; althouh, as they are non-conductive, electropolishin is not one of them. Startin from a bulk material, an arbitrarily thin slice can be cut away with a diamond waferin blade. Once a thin piece is obtained, one side is polished and lued to a lass slide. The exposed side is then round down with SiC paper until it is 100µm thick. Next, a 3mm disk can be ultrasonically machined from it usin an ultrasonic drill and some ceramic abrasive powder. This disk will then have to be dimpled, which involves usin polishin paste on a rotatin wheel to ently wear a bowl-shaped recess into one side of the disk. This process reduces the thickness of the sample and makes it ready for the final and slowest part of the procedure: ion beam millin. If a beam of eneretic ions is directed at a solid, atoms can be knocked out of the solid in the process known as sputterin. The ion uns commonly used in ion beam thinners enerate a plasma by strippin electrons from low-pressure aron atoms in a hih electric field. The electric field also accelerates the ions throuh an aperture in the cathode, producin a beam which is directed onto the TEM sample. Two uns are usually used so that the sample can be thinned from both sides simultaneously, and the sample is rotated to prevent surface rouhness from developin. Aain, eventually a hole will appear in the sample, and the reion around this hole should be thin enouh for examination in the TEM. If no ultrasonic drill is available (or if time is short), it is possible to thin the sample by hand to the point where it starts to fall apart. Once the sample starts to fall apart or wear unevenly, it is polished ently. A 3mm support rin (usually copper) is lued to the surface, and the sample is floated off the lass slide by applyin heat. The sample is typically so delicate by this point that the excess around the copper rin can simply be broken off, and the ceramic-copper assembly can be placed in the ion beam thinner with or without dimplin. B. Oranic samples The preparation of oranic materials for the TEM is very complex and typically involves the use of several very toxic materials. The method starts by fixin the sample by soakin it for 30mins to two hours in chemicals like paraformaldehyde, lutaraldehyde, and CaCl in cacodylate buffer. The sample is then washed for mins in a CaCl-containin cacodylate solution and postfixed for one - two hours in osmium tetroxide. Potassium ferricyanide can also be added for lycoen and stroner stained lipid membranes. The sample is then washed with distilled water, R. Ubic 1

2 treated in the dark for one - two hours with aqueous uranyl acetate, and washed aain, at which stae the sample is finally fixed. The next step is to dehydrate the sample. In order to minimise lipid loss and shrinkae, dehydration is done in staes by soakin the sample in solutions of either ethanol or acetone of increasin concentration (10-0 mins soak in 70% ethanol followed by 10-0 mins soak in 90% ethanol followed by mins soak in 100% ethanol). Afterwards, a five-minute soak in a 1:1 mixture of ethanol and propylene oxide followed by a 10-minute soak in pure propylene oxide will complete the dehydration process. The fixed and dehydrated sample is then ready to be embedded in epoxy, usually consistin of a polymer resin (e.., araldite CY1), hardener like dodecenylsuccinic anhydride (DDSA), plus an accelerator like benzyldimethylamine (BDMA). Over the course of the next few days, the sample is embedded with this resin in a suitable mould and left in an oven at 60 C for 48 hours to complete the polymerisation. Once complete, thin slices can be sliced off the embedded sample with a microtome, which is an apparatus used to cut thin sections of a specimen with a knife that is made of either steel, lass, sapphire, or diamond. The thin sections are then collected onto a copper support rid, coated with carbon if necessary, and examined in the TEM. Imae contrast in the TEM TEM imaes are simply manified imaes of the electron intensity on the bottom surface of the specimen and contrast arises only if the intensity varies sinificantly from one reion to another. A. Absorption contrast We have already examined this mechanism whereby samples which are thicker, denser, or with hiher atomic number allow fewer electrons to pass throuh (they absorb and scatter more of them). It applies to both amorphous and crystalline specimens and is used extensively by bioloists who call it mass-thickness contrast (a poor name, as it inores the atomic number component especially as they usually stain their samples with a heavy metal to decorate features of interest). In crystalline samples, this contrast mechanism is usually swamped by others. 1. Imain voids/pores/bubbles/cavities Pores in specimens are examined in the TEM usin defocused contrast microscopy. Small cavities are most visible if the specimen is imaed in a defocused mode, i.e., if the imae plane of the objective lens deviates from the bottom surface under kinematical conditions (s >> 0 or very thin). Theoretical calculations show that the centre of the dark frine of an underfocused cavity defines its true projected ede.. Local chane in density The small cavity is an extreme case of a local chane in density of the sample. Under kinematical conditions the imae arises from mass-thickness contrast and the cavity appears lihter than the backround in a BF imae (see below). This effect may be small and a more noticeable effect miht be Fresnel frines due to defocusin; however, in dynamical conditions R. Ubic

3 (s = 0 or thick) the reion of specimen containin the pore is appreciably thinner than its surroundins and the pore may show contrast arisin from thickness frines (see below). B. Diffraction Contrast Diffraction contrast is simply a function of the diffraction conditions. It is the method most commonly used to study crystal defects like dislocations, stackin faults, precipitates, etc. It is the mechanism which explains extinction (bend) contours and thickness frines. 10 nm Carbon Lead 0 nm θ B 9% 91% 17% 83% 96% 4% 100-0% 0-100% Sample Objective Aperture Electron Beam Objective aperture removes scattered off-axis beams Objective aperture removes diffracted beams R. Ubic 3

4 1. Briht-field (BF) and dark-field (DF) imain Typically, to simplify TEM analysis we require only one set of planes at the Bra condition so that there is only one set of reflectin planes. To achieve this it is necessary to orient the sample in such a way that only a sinle diffraction spot is excited. This reflection, toether with the transmitted beam (which is the un-diffracted intensity and is always present in diffraction patterns) ives us what is called a two-beam condition. B = [110] = 0 = 111 = 113 = 00 For a briht-field imae, the objective aperture is placed around the transmitted beam, excludin the diffracted one. The vector from the transmitted beam (000) to the diffracted one (hkl) is called. For a dark-field imae, the incident electron beam is tilted so that the diffractedd beam is parallel to the optic axis by usin deflectors. In fact, it is ( h kl ) which is brouht to the centre, and the associated vector is therefore. R. Ubic 4

5 I o I o object θ objective lens θ T objective aperture T I t Briht field I d =I o -I t Dark field. Perfect crystals If a beam of electrons is incident upon a crystal of thickness t, the diffracted intensity for a iven reflection can be calculated as: I πsin = ξ πs ( πts) where s is the deviation parameter (the deviation of the vector from the Ewald sphere, or the distance in reciprocal space from the exact Bra condition) and ξ is a material constant (for a iven ) called the extinction distance. Althouh the maximum diffracted intensity will always be for s = 0, some diffraction will also occur for s 0. The thinner a crystal is, the further it can deviate from the Bra condition and still diffract. This rule (which is also true for other forms of diffraction, e. XRD) can be thouht of with reference to the shape and size of the rel rods in reciprocal space and their intersections with the Ewald sphere. As the crystal thickness increases, the rel rods become shorter and so make fewer intersections with the Ewald sphere there are fewer reflections in such diffraction patterns. Absorption and increased inelastic scatterin also means such patterns show more diffuse scatterin and eventually, when the thickness is too reat, no intensity at all ets throuh. The extinction distance is iven by: ξ = πv cosθ c λf B where V c is the volume of the unit cell, θ B is the Bra anle, λ is the electron wavelenth, and F is the structure factor. The amount of contrast in a specimen, the apparent size of a defect, the appearance of stackin fault frines, thickness frines, and bend contours are all determined by ξ. R. Ubic 5

6 In eneral, sharp imaes are only obtained when ξ is small (a few tens of nm). Accordin to the equation above, in order to minimise ξ, θ B must be made small and F lare. These two conditions are only satisfied for low-index reflections. a. Bend contours A plot of I versus s is called a rockin curve, since variation in s can be achieved by rockin a flat specimen throuh the Bra condition. Such a rockin curve is shown below. The yellow curve represents the equation as iven above, which is only valid for very thin crystals where the intensity of diffracted beams is neliible (kinematical conditions). The orane curve allows for dynamical effects, and the red curve allows for both dynamical effects and absorption. Intensity of Diffracted Beam t/ξ = 1.5 ξ /ξ = 0.1 ξ /ξ o = Deviation Parameter (nm -1 ) A buckled specimen provides a rane of s values without the need for rockin and so produces frines just like a rockin curve. The bend or extinction contours which result often reflect the symmetry of the crystal and, in fact, have been used in the past to orient crystals. Dark-field bend contours in Pb 3 Nb O 8. Bend contours can easily be distinuished from actual crystalline defects by tiltin the specimen. Bend contours will seem to sweep across the specimen as it is tilted and different planes are brouht into the Bra condition. Actual defects will not appear to move like this, althouh their appearance will chane as the specimen is tilted. R. Ubic 6

7 In eneral, BF and DF imaes of bend contours are non-complementary. BF intensity depends on the sin of s, whereas the DF does not. In addition, where s is small and positive, there is a reion of hih intensity in BF due to anomalous absorption (defined below). Where s is neative, overall transmission is low in BF. The hihest intensity for DF imaes occurs when s = 0. b. Thickness frines From the equation for I above, it can be shown that I varies periodically with t, becomin zero each time ts is an inteer. A typical wede-shaped specimen shows thickness frines. The fiure below demonstrates this effect. The yellow curve represents the kinematical theory, which predicts that intensity simply rises with thickness. The orane curve represents the more realistic dynamical case, and the red curve shows the additional effect of absorption. Intensity of Diffracted Beam ξ ξ = 100 nm ξ /ξ = 0.1 ξ /ξ o = 0.1 w = 0 (s = 0) Thickness (nm) If a crystalline specimen is thicker than about one third the extinction distance, then there will be appreciable interaction between the electron beams as they travel throuh it. Such interaction R. Ubic 7

8 renders the kinematical theory inadequate and a dynamical theory is needed. The most straihtforward form of this theory only considers interactions between the transmitted beam and one diffracted beam defined by the reciprocal lattice vector. The Howie-Whelan equations can be used to describe the amplitude of both the diffracted (φ ) and undiffracted (φ o ) beams as a function of z, the distance throuh the crystal: dφ dz dφ dz o iπ = φ ξ o iπ = φ ξ o o iπ + φ ξ iπ + φ ξ o exp exp ( πisz) ( πisz) The first term arises from the scatterin from the transmitted beam and the second from the diffracted beam. The amplitude of each wave chanes with z due to contributions from the other. The factor ξ o is the atomic scatterin amplitude for zero anle and is a measure of the refractive index of the material. In order to calculate the intensity, the equations must be interated over the entire thickness, t, to ive φ o and φ at the exit surface of the specimen. The briht-field intensity is then iven by φ and the dark-field intensity by * φ, where * indicates the complex conjuate. The * o φ o intensity of the diffracted beam is then: φ I πsin = ξ πs' ( πts' ) which is exactly the same as the kinematical solution except for the use of the effective deviation parameter, s, where: s' = s + ξ 1 To account for the effect of s on ξ, we define the effective extinction distance: ξ eff = ξ 1+ s ξ where sξ = w is the deviation from the Bra position in a dimensionless form that is more convenient to use than s. Note that frines only occur at exactly the extinction distance ξ when s = 0. If s 0, then the effective extinction distance ξ should be used. In order to model correctly the effects of absorption on: eff R. Ubic 8

9 - the observed decay of thickness frines with thickness - the non-complementary nature of BF/DF imaes we must account for absorption (hih-anle inelastic scatterin). The possibility of absorption can be accounted for by replacin 1/ξ with the complex parameter 1/ξ + i/ξ '. ' ξ is responsible for the overall decrease in intensity with increased Linear absorption ( o ξ o ) ' sample thickness, while anomalous absorption ( ) ξ involves selective absorption of certain electrons within the crystal. Anomalous absorption is responsible for some of the important ' ξ are found ξ depth asymmetries of the imaes of many crystal defects. Values of ( ) ξ empirically by matchin theoretical and experimental imaes and are typically Althouh thickness frines are predicted by both kinematical and dynamical theories, their appearance in each is very different. Under kinematical condition (s >> 0) the frines are closely spaced and limited to thin reions near the hole. The frines are stroner in the DF imae than in the BF (i.e., they are non-complimentary), and the contrast from defects is low. Conversely, under dynamical conditions (s = 0) the frines are broader with reasonably complimentary BF and DF imaes. The defect contrast is stron and the best defect imaes occur just as the frines damp out. c. Overlappin rains If one rain oriented in a two-beam condition overlaps another which is not, then the first rain can show thickness frines just as if it were a tapered sinle crystal (which it is). Such frines will be parallel to the intersection of the rain boundary with the surface and can easily be distinuished from stackin fault frines by dark-field imain, in which case only the stronly diffractin rain will appear briht. When both crystals are stronly diffractin, moiré frines may appear. These are common in imaes of thin crystalline materials deposited on each other, where two crystals are diffractin with slihtly different values of or are rotated slihtly with respect to each other. In the case of parallel lattices, the net effect is a set of frines runnin perpendicular to with a spacin: D p = d d d 1 1 d and in the case of lattices only rotated by an anle α, the spacin is: d D r = sin 1 ( 1 α ) R. Ubic 9

10 d 1 d D p Parallel Moiré Patte rn + = d 1 d 1 Rotation Moiré Patte rn + = D r In eneral, lattices could be rotated and have different spacins, in which case: D = d 1 + d d d 1 d1d cosα d. Converent beam electron diffraction (CBED) CBED is a powerful tool for probin the crystalloraphy of a small specimen as well for analysin local strains and thicknesses. Conventional diffraction is performed usin nearlyparallel electron beams (parallel illumination), and so ives rise to diffraction spots. The CBED technique involves focusin the incident illumination down to a fine point, and so yields diffraction discs. Conventional selected-area diffraction patterns are limited spatially. The typical diameter (D) of a selected-area aperture is 5-100µm. The manification (M) of the objective lens is typically x40, so the diameter of the selected reion of the imae is D/M = 5µm/40 = 0.15µm. Consequently, it is not possible to select an area on the sample smaller than ~0.15µm from which to obtain crystalloraphic information. In addition, possible errors in selected-area diffraction can arise if the imae and SA aperture are not coplanar due to focusin errors. These errors could be due to one of three factors: - The SA aperture may not be focused on the imae plane by the diffraction lens (in which case the aperture imae will appear fuzzy). - The imae itself may not be focused correctly on the imae plane by the objective lens. Since the plane of focus is not on the specimen plane but displaced from it by a R. Ubic 10

11 distance d, information from outside the area defined by the SA aperture will appear in the diffraction pattern. - Spherical aberration of the objective lens, C s, can result in off-axis rays bein focused nearer to the lens than are axial rays. A A α specimen objective lens Error = C s α 3 B C B C SA aperture In this case, information from AA for off-axis rays oes to CC instead of BB as occurs for axial rays near the centre of the objective lens. The combined error (Y) from these sources can be lare: Y = dα + C s α 3 where d = defocus, α = scatterin anle, and C s = spherical aberration coefficient. For α = θ = rad, C s = 3.5mm and d = 3µm, Y = 0.18µm, which makes a 5µm SA aperture selectin an area of 0.15µm completely inaccurate (the error 0.18µm > 0.15µm the diameter of the selected reion). We usually don t use a SA aperture smaller than 50µm due to these lare errors, which limits the reion from which reasonable crystalloraphic information can be obtained to about 1µm. The SA aperture sizes available in the JEOL JEM-100 HR instrument are 10µm, 0µm, 50µm, and 100µm. If crystalloraphic information is needed from smaller areas then microdiffraction or converent beam techniques should be used. i. Method This technique ives area selection to less than 1nm by converin the incident beam onto the sample, requirin a combined condenser/objective lens system. Historically, the first condenser lens system in the TEM (1940s) consisted of a sinle lens. Later, in the 1950s condenser lens systems contained two lenses, a stron C1 lens (spot size) and a weaker C lens (brihtness), with the first demanified source imae occurrin at the cross-over between them. In the 1960s Riecke and Ruska added a C3 (upper objective) lens, allowin the creation of a small (<< 1µm) beam with a converence semi-anle (α) > 10mrads. The converence anle is controlled by the R. Ubic 11

12 size of the condenser aperture, which controls the size of the discs. This relationship is interactively demonstrated at Incident Electrons Specimen Diffraction Discs Because of the extreme intensity of the focused incident beam, the specimen used must be very stable aainst the radiation. The specimen will become very hot in the reion of the fine probe, and so coolin is enerally required to prevent thermal diffuse scatterin from obscurin the fine detail within the discs. For the same reason, a very hih vacuum system is required to prevent dirt (mostly carbon) from bein deposited on the specimen surface. Additionally, the tiny reion examined must be defect-free and, if crystalloraphic information is required, of uniform thickness. Clearly, CBED is not a trivial operation, and the interpretation of CBED patterns is no less difficult! From CBED imaes it is possible to obtain local specimen thickness (useful when, e.., determinin defect densities), strain, and crystal structure (even a full space roup determination). ii. Features of CBED patterns In eneral, CBED patterns contain three types of useful information: - diffraction discs in the ZOLZ - diffraction discs in the HOLZ - HOLZ lines within the diffraction discs arisin from diffraction from HOLZs. The position of HOLZ lines is sensitive to lattice parameters and they can be used to determine both the lattice parameters and effects on them due to strain or chemical composition. [111] CBED pattern from Cu R. Ubic 1

13 iii. Thickness determination In a thin (kinematical) sample there is no information in the discs; however, in thicker reions of the sample, dynamical effects become important and ive rise to features within the discs. Eventually, the sample is too thick and absorption masks all the useful information. The frines present in the diffracted disc at intermediate thicknesses can be used to determine the local sample thickness. They arise because ξ is a function of thickness, t. As the electron beam oes throuh the specimen thickness t, the parts at various s interfere to ive frines. The width of the frines depends on t accordin to: si ni 1 = ξ 1 ni 1 + t where n i is an inteer and s i is: s i λ θ i = d hkl θ where θ is the Bra anle, θ i is the distance between frine i and the dark Kikuchi line throuh the diffracted disc. S>0 S<0 S>0 S<0 θ 1 θ X θ θ 3 Plottin (s i / n i ) vs (1 / n i ) results in a line whose slope is -(1/ξ ) and whose y-axis intercept is (1 / t). Such a plot enables t to be determined. R. Ubic 13

14 This technique is accurate to about 1 - % for thickness measurements and is very useful in quantitative defect analysis, e..,, determinin the number of defects per volume (defect density). iv. Crystalloraphic information It is possible to extract a reat deal of crystalloraphic information from CBED patterns, even a full space roup determination; however, such techniques are seldom used as the imaes are difficult obtain and even more difficult to interpret. The advantae is that it is theoretically possible to determine the space roup of crystals much smaller than the lare sinle crystals used to determine structures via x-ray diffraction. As this method typically involves the use of a cryo- to perform at double-tilt holder, which the BSCMC does not have, it is not technically possible BSU. For this reason, the technique will only be covered briefly here. A space roup determination proceeds accordin to the followin steps: 1. Obtain at least two low-index CBED patterns, includin both ZOLZZ and HOLZ. If HOLZ information is not visible, it may help to reduce the camera constant.. Determine the symmetry of both the ZOLZ (includin HOLZ information) and whole pattern in each case. 3. A standard table is used to convert the observed ZOLZ symmetryy to a projection diffraction roup and possible diffraction roup. There are 10 possible projection diffraction roups and 31 possible diffraction roups. 4. The same table is used to convert the whole-pattern symmetries to possible diffraction roups from amonst those defined in (3). R. Ubic 14

15 5. Another standard table is then used to correlate diffraction roups to one of the 3 real crystal point roups. 6. The point roup common to all CBEDs is the true point roup of the crystal. Several CBED patterns may need to be taken for unambiuous determination of the point roup. 7. The space roup can then be determined by examination of a forbidden reflection ( f ) which occurs due to double diffraction. Some of these reveal dynamic absences (dark bars within the disk) which imply the presence of lide planes or screw axes. Alternatively, if another forbidden reflection is observed on tiltin parallel to f, then a lide plane is present. If f disappears then re-appears on tiltin parallel to f, then there is a -fold screw axis. Thus, the space roup can be determined. 3. Defects A defect which disturbs the crystal planes will locally modify the deviation parameter. In this case, the Howie-Whelan equations can be re-written as: dφ dz dφ dz o iπ = φ ξ o iπ = φ ξ o o iπ + φ ξ iπ + φ ξ o exp exp ( πi( sz + R) ) ( πi( sz + R) ) where R is the displacement of atoms from their lattice positions due to the defect (e., a Burers vector), and R modifies the product sz. When R = 0 (or an inteer), the defect has no effect on the diffractin planes and so it is invisible. This condition is called the invisibility criterion, and occurs when is perpendicular to R. Stackin faults, rain boundaries, and phase boundaries can all be studied in this way. The larer R is, the more obviously visible will be the defect. The distortion of the lattice due to the defect causes an extra phase factor, exp(iα) in BF and exp(-iα) in DF, to be superimposed on the normal scatterin process for perfect crystals, where α = π R The defect imae is therefore a function of, s, R, z, and ξ. a. Linear defects: Ede dislocations Contrast can also arise from dislocations. Planes around the dislocation core are usually distorted quite severely, so if a crystal is oriented into a two-beam condition with s 0, the planes on one side of the core will be bent throuh s = 0 and so stronly diffract. If two imain conditions can be found for which the dislocation is invisible ( b = 0 ), then b can be determined by takin the cross product b = 1. This condition is true all alon the dislocation line, which then appears as a dark line in a briht-field imae. This arument is valid for screw dislocations (b dislocation line u), but for ede (b u) or mixed dislocations, it is R. Ubic 15

16 slihtly less straihtforward. complicated. The analysis for partial dislocations is also somewhat more Dislocations in nickel 1 Å Examinin the fiure below which contains a screw dislocation with b parallel to u, it is apparent that if we look down a direction parallel to b and u, the projection appears undistorted by the dislocation. Planes which contain this direction include (010) and (001); therefore, by imain with = 010 or = 001, then the electrons will see no bent planes and ive rise to no diffraction contrast. The displacement due to the dislocation is perpendicular to, so b = 0. z x y On the other hand, if we look down the [010] or [001] directions, it is easy to see that the projections will be distorted. The (100) plane contains both of these directions; therefore, by imain with = 100, the electrons will see the bent planes and ive contrast. A b analysis enables us to determine the direction of b. The steps are: 1. Tilt to a zone axis, record and solve the pattern. This will identify the vectors which are operatin. R. Ubic 16

17 . From this orientation, tilt to a variety of two-beam conditions and record BF/DF pairs and SADPs. 3. If a dislocation oes out of contrast (disappears) for a particular, then in that case b = For an unambiuous assinment of b, two vectors for which b = 0 are required. The direction of b is then found by takin the cross product b = Often a b table is constructed showin the vectors used and likely bs for the crystal structure bein anaylsed. This identification of b is actually a bit more complicated because dislocations appear out of contrast when b < 1/3. Similarly, dislocations may not be invisible even if b = 0 when b u 0 (u is the unit vector alon the direction of b). b. Planar Defects It seems there is some ambiuity in the cateorisation of planar defects. If the characteristics of planar interfaces are derived from crystalloraphic (symmetry) considerations only, then three cateories of interface can be defined: i. Translational interfaces (α boundaries) These boundaries separate two parts of a crystal that are related to one another by a constant displacement vector R, independent of the distance from the interface. An α boundary is an interface that produces a phase factor of α = π R and enerally with s equal on either side of the boundary, i.e., the orientation is the same on both sides. The value of α can rane from 0 to π, dependin on R. The symmetry and characteristics of the contrast in the imae depend on the value of α, which depends on and R. The further classification of the boundary type is based on the value of α. In this type of defect, a translation occurs across the boundary and leads to phase interference between the two parts of the crystal. The resultin imaes consist of alternate briht and dark frines runnin parallel to the intersection of the boundary with the surface. The BF imaes are symmetric while the DF imaes are asymmetric. These frines can be thouht of as resultin from the interference between the beams diffracted in the upper part of the crystal, above the fault, and those diffracted below the fault. The diffracted waves undero a phase chane at the fault and the frines are thus the usual manifestation of the interference between two sets of waves which are slihtly out of phase. top BF DF bottom sinα < 0 R. Ubic 17

18 These frines are produced by stackin faults, APBs, or planar precipitates. They result in defect frines which are identical in contrast in both briht-field and dark-field imaes above the fault but complementary below it. Note, the contrast will be reversed if usin the displacedaperture technique because then hkl will be operatin instead of -h-k-l. Stackin faults, rain boundaries, and phase boundaries are planar defects which are frequently studied in projection as they cross the thin TEM specimen. In eneral, the term stackin fault is applied to crystals which can be constructed from stacked planes; therefore, they possess specific values for R. An APB is a translation interface with a displacement vector R equal to a vector connectin different atom species in the unit cell. Stackin faults occur only on close-packed planes; APBs can, in principle, occur on any plane and need not be planar. APBs can also accommodate nonstoichiometry within the boundary reion. APBs can form between ordered and disordered structures as well as between two ordered structures. APBs are almost always thouht of as havin α = π symmetrical frine contrast (π boundaries are a special case of α boundaries in which α = π) because the pioneerin work into the contrast effects of APBs was conducted on CuAu, an alloy in which the phase chane associated with the APB is α = π; however, APBs with the values +/-(1/3)π, +/-(1/)π, and +/-(/3)π for α have also been demonstrated. Summary: α 0, s 1 = s = 0 (δ = 0) ii. Twin interfaces (δ boundaries) These boundaries separate orientational variants which possess a displacement field in which the displacement vector R increases linearly with distance from the interface. In other words, they separate two reions of a crystal with slihtly different values of or s for the same operatin reflection, i.e., a sliht misorientation of reflectin planes toether with possible differences in ξ. These boundaries typically arise as a result of an orderin process that differently distorts two parts of the crystal. Other examples are reflection and rotational twins and 90 ferroelectric domain boundaries in BaTiO 3. In this case, the small tetraonal distortion (c/a = ) associated with the paraelectric (cubic) to ferroelectric (tetraonal) transformation means that the same planes can contribute to diffraction with different deviations (w1 and w) from the Bra condition. R. Ubic 18

19 Frine contrast arises at the boundary because of the difference δ = w1 - w. Since w = sξ, the behaviour of the frine patterns depends on both s and ξ. In this case, the frine contrast differs from that of α boundaries in that the BF imaes are asymmetric and the DF ones are symmetric. top BF DF bottom w > 0 Summary: α = 0, w = w 1 - w = s 1 ξ 1 - s ξ = δ 0 iii. Inversion interfaces These defects relate one domain to another domain by an inversion operation. The 180 inversion domain boundaries (IDBs) in BaTiO 3 and PbTiO 3 are ood examples and will produce frines like α boundaries. Some confusion exists concernin the definition of and distinction between IDBs and APBs, and IDBs have frequently been called APBs. A major reason for this confusion is due to the different definitions used to describe an APB, which sometimes allows an IDB to be considered as a type of APB. These three cateories are defined in terms of symmetry and also describe the eometry of the interface. If, alternatively, the interface is described in terms of the electron wave and interference effects, then any boundary across which a phase chane occurs is termed an APB. c. Trace analysis i. Linear defects Trace analysis is a way of combinin the crystalloraphic information in the selected area electron diffraction pattern with the eometry of the microraph to deduce details about defects like interfaces, precipitates, stackin faults, dislocations, etc. The direction of a line feature (straiht dislocation lines, needle-shaped precipitates, etc.) can be determined by correlation with the diffraction pattern. The projection of that line [uvw] on the plane perpendicular to the electron beam can first be determined. Then, the actual line of the defect must be contained in the plane (hkl) that contains the projection [uvw] and is parallel to the electron beam direction. For example, a line defect can be uniquely characterized as follows. We will assume that a [111] defect exists in a cubic crystal. Tiltin so that the beam direction is [001], we observe both an imae and the correspondin [001] diffraction pattern (both shown schematically below): R. Ubic 19

20 As we can see, the trace is [u 1 v 1 w 1 ] = [110] on the (001) plane. Therefore, the defect direction must lie on a plane (h 1 k 1 l 1 ) which both contains the projection [110] direction and is parallel to the beam direction. The eometrical relationship can be expressed as: h k l 110 = h k l 001 = h l 1 1 = k = 0 1 Since the normal to (h 1 k 1 l 1 ) is therefore perpendicular to both [110] and [001], it is handy to use the cross product: iˆ det = [110] 0 ˆj 0 kˆ 1 The plane (h 1 k 1 l 1 ) normal to this direction is, of course, ( 1 10). We can visualize what's oin on as shown below. Electron beam (110) [111] (001) [110] R. Ubic 0

21 In this case then (h 1 k 1 l 1 ) = ( 1 10). Of course, the same plane would be derived if the beam direction had been [110] and the trace [001]. Unfortunately, there are an infinite number of directions on this plane (e.., 111, 11, ). So, we need to use the same method to find another plane, then the direction we're after will be the zone axis of these two planes (the direction both planes share in common). Note that the direction [111], which is also contained in the ( 1 10), does not make sense as a solution, as it would imply a trace of zero lenth (lookin at the defect head-on in this orientation). The same defect viewed parallel to [ 111] would have a trace of [11], as we see below: Therefore, the defect direction must lie on a plane (h k l ) defined by: h k l h kl 11 = = 0 h h = k + l = k l Aain, we can use the cross product to uniquely define (h k l ) as: iˆ ˆj kˆ det = [011] 1 1 The plane (h k l ) normal to this direction is, of course, ( 011). Aain, we can visualize what's oin on as shown below: R. Ubic 1

22 Electron beam [111] (011) (111) [11] So, the plane which satisfies these conditions is (h k l ) = ( 011). Aain, there are an infinite number of directions on this plane, but only one will also be contained on ( 1 10). It can be found by aain takin the cross product: iˆ det = [111] 0 ˆj 1 kˆ 1 (110) [111] (011) So, the defect is now uniquely defined as residin in the [111] direction. ii. Planar defects Planar defects are most successfully characterized by analyzin their trace or line of intersection [uvw] with the sample surface, possibly combinin such an approach with a R analysis. As for linear defects, traces can be deduced by correlation of imaes with their correspondin diffraction patterns. In the example below of planar defects in an FCC material, there are two sets of defects, each residin on a different plane. We must first assume that both sets of defects are essentially the same kind of defect and that they reside on the same {hkl} planes. R. Ubic

23 (111) 044 (111) [101] [110] 00 nm 00 nm Both microraphs have been taken close to the [111] zone axis, as shown in the SADP, but usin different reflections to form dynamical briht-field imaes. On the left, the ( 440) spot has been used, and the traces which remain in contrast are parallel to [ 101]. On the riht, the ( 404) spot has been used, and the traces which remain in contrast are parallel to [ 110]. Considerin first the left-hand side, the traces which are visible here parallel to [ 101] ; therefore, the plane which produced them must contain this direction. Such planes are of the form {1n1}. The R analysis tells us the same thin. The traces which are visible here are invisible when = 404 ; therefore R = hkl = 0 h = l Here we can use hkl as the displacement vector R because planar defects on the (hkl) plane will cause displacement in the [hkl] direction. The manitude of the displacement is not relevant. Aain, planes which satisfy this condition are {1n1}. As the trace of these planes is [ 110], any plane of the form {11n} could have caused it. Aain, the R analysis tells us the same thin. The traces which are visible here are invisible when = 440; therefore R = hkl = 0 h = k Planes which satisfy this condition are cubic {11n} which are, of course, equivalent to {1n1}. R. Ubic 3

24 Now, it can only be said with certainty that the defects lie on {11n} planes, which may be {110}, {111}, {11}, etc. In order to uniquely identify the plane, it is helpful to find an orientation which is ede-on (perpendicular) to the defects. The hih-resolution microraph below is such an imae. It shows defects perpendicular to the (110) plane. 50 Å The defects have a trace of [ 11]. So, we know that the planes contain both [110] and [ 11] directions, which is sufficient to uniquely identify it as follows: iˆ ˆj kˆ det = [1 11] 1 1 The plane which is perpendicular to this direction is, of course, ( 111). So, the defect planes must lie on {111} planes, makin the defects in the BF imaes above ( 111) and ( 111), respectively. d. The Column Approximation When examinin crystal defects in the TEM we invoke the column approximation, which basically assumes that the wavelenth of the imain electrons approaches zero. This approximation allows the intensity on the bottom surface of the crystal to be obtained by calculatin independently the intensity at the bottom of columns about nm across. For a stackin fault, if we inore local strain, then in each column the displacement vector R is effectively zero above the fault but will have a constant non-zero value everywhere below it. If the fault is a simple displacement (translation), such as the common stackin fault in FCC metals, then the value of s is the same above and below the fault, as no lattice planes are tilted by the fault. If the fault has a misorientation associated with it, then the value of s will chane abruptly at the fault plane. Faults ivin rise to both displacement and misorientation, in which both s and R chane at the fault, can occur. R. Ubic 4

25 As in dislocation analysis, if R = 0 (or any inteer) then the direction of the displacement vector can be determined usin the invisibility criterion. To fully characterise the defect, three non-coplanar reflections are required for which it oes out of contrast. Imae simulation is also often used. In eneral, frine contrast alone is often not sufficient to identify the type of defect (stackin fault, APB, IDB, etc.) or to accurately determine its R; therefore, to accurately determine the manitude of the displacement and the defect type, simulation of experimental imaes is often required. e. Stereomicroscopy When usin diffraction contrast imain, it is essential to chane only the specimen orientation while maintainin s and identical for the two microraphs. This is best achieved by tiltin from one side of a zone axis to the other usin the Kikuchi map. The two imaes are then inserted into a stereoviewer, comprised of two mirrors and binoculars, with the vector, which is the tilt axis used to obtain the microraphs, perpendicular to to the line joinin the viewer s eyes. The apparent heiht difference (parallax) measured on the viewer (d) is related to the real heiht difference H throuh the tilt anle θ and manification M: H = d M sinθ This technique can be used to determine whether features are on the surface or in the bulk, their depth in the sample, and the sample thickness. Sections of conventional thickness (50-100nm) are essentially two-dimensional structures and have little information in the z direction. Sections considerably thicker (0.5-1µm) must be used in order to have enouh three-dimensional structure for effective stereo viewin. Of course, thick sections present problems due to increased electron absorption and inelastic scatterin. C. Phase contrast 1. Lattice imain Unlike absorption and diffraction contrast mechanisms, which rely on the amplitude of scattered waves, phase contrast results whenever electrons of a different phase pass throuh the objective aperture. If spots alon a systematic row are allowed throuh, a lattice imae is formed. Such imaes can be used to show the extent of crystallisation of a rain-boundary film or the habit plane of planar defects. If more diffracted beams are allowed to contribute, then a structure imae can be formed. Interpretin such imaes is not trivial and requires knowlede of specimen thickness, defocus, and TEM resolution (itself dependent on C s of the objective lens and wavelenth). To fully understand hih-resolution structural imaes, a series of imaes must be obtained and compared to a simulated series of imaes enerated by inputtin the likely crystal structure into a sophisticated software packae. R. Ubic 5

26 How many of you were told, perhaps durin your first science lessons at school, that atoms are too small to see? Indeed, with typical diameters of m, atoms were for a lon time considered articles of faith by many scientists. We cannot see atoms, we are later tauht, because diffraction places a fundamental limit on the resolution of an imae. Rouhly speakin, we cannot see anythin smaller than the wavelenth of the liht used to produce the imae, and since the wavelenth of visible liht is some 10,000 times larer than the typical distance between two atoms, we cannot see individual atoms; however, other forms of electromanetic radiation have much shorter wavelenths than visible liht. The x-rays used in crystalloraphy, for example, have wavelenths of less than a nanometre. The problem is that it is extremely difficult to focus x-rays. Luckily, quantum mechanics provides an alternative way to view the microscopic world: subatomic particles like electrons. In diffraction (amplitude) contrast imain, in eneral, only one beam is used to form the imae (i.e., the transmitted beam in BF or a diffracted beam in DF) so that any phase relationship between the beams is lost. If the transmitted and diffracted beams can be made to recombine (thus preservin their amplitudes and phases) a periodic frine pattern (lattice imae) of the diffractin planes is formed by phase interference between the two beams. This technique usually requires a lare objective aperture nm. Hih resolution imain In order to resolve atoms, it is necessary to have the smallest possible objective lens focal lenth and aberration coefficients. If the diffracted spots from several systematic rows at a zone axis are included in the objective aperture and used to form the imae, a structure imae of individual rows of atoms may be resolved. The principle in this case is the same that of the Abbe theory for ratins in optics. R. Ubic 6

27 [111] [11] [001] [11] 111 [110] 50 Å Pb 1.5 Nb O 6.5. Defocus = -80nm, thickness = 3nm. 50 Å Overlappin <101> SADPs of Sr Ta O 7 showin (00) spacins (d = Å) of two twin variants sharin a common (151) habit plane. Both hih-resolution lattice and structural imain are examples of phase imain. Considerin the case of just two beams to form the imae, in order for the effect of recombinin two out-ofphase waves to be visible in the hih-resolution electron microraph (HREM), the amplitudes of the resultant wave (sum of transmitted and diffracted beams) must be different to that of the transmitted beam. The transmitted beam will have a much stroner intensity and so constitutes the backround of the imae. The reatest chane in amplitude (and therefore the reatest contrast in the imae) corresponds to the case where the two beams are perfectly in phase. The result is atoms which appear white on a black backround. A 90 phase shift causes no chane in intensity and therefore no contrast. A 180 phase shift results in a sum wave which is lower in amplitude than the transmitted wave, yieldin black atoms on a white backround. The microscope introduces some additional phase shifts which complicate this simplistic picture. R. Ubic 7

28 phase difference of 0 incident scattered sum 0 π π 3π 4π 5π 6π white atoms dark backround phase shift of 90 incident scattered sum 0 π π 3π 4π 5π 6π no contrast R. Ubic 8

29 phase shift of 180 incident scattered sum 0 π π 3π 4π 5π 6π dark atoms white backround A lare objective aperture is required to allow the beams to interfere and form the imae. The imae must also be off the objective focus position to utilise Fresnel (defocus) diffraction. To achieve hih resolution, a lare voltae is usually necessary ( 00kV). The proper conditions for formin structure imaes which best represent the structure of the specimen must be chosen by comparin imaes obtained in the microscope with computed imaes based on the dynamical theory (e.., multislice calculations). For interpretable imaes we need: 1. very thin (about 5nm) specimens. If they are too thick, inelastic scatterin derades the phase contrast information.. to be at a zone axis so that many beams are available and the crystalloraphic information is interpretable. Only those diffracted beams which correspond to distances within the point resolution of the HREM will contribute to the imae. 3. precise alinment of the electron beam down the optic axis. Also, any defects must lie alon the beam direction. 4. coherent illumination (i.e., LaB 6 filament or FEG). 5. a specific value of objective defocus. In order to establish this value, the quantitative defocus associated with each click of the objective focus control must be calibrated. As the imae obtained is a function of a number of variables, these must be defined and calibrated in order to interpret the imae. 1. Sample thickness. Objective lens defocus R. Ubic 9

30 3. Microscope parameters like kv, Cs, Cc, etc. 4. Number and type of beams included in the objective aperture. 5. Beam tilt Interpretin imaes of reions inevitably of varyin thickness and at different values of defocus is complex because the objective lens is imperfect and itself introduces phase shifts into hihanle information. This problem is formally expressed in terms of the contrast transfer function (CTF) of the objective lens, which is effectively a map of the phase shift includin the microscope effects. It ives a measure of the atom contrast (+1 = briht, 0 = invisible, -1 = dark) as a function of atom spacin, but a detailed description of the CTF is beyond the scope of this class. 3. Lorentz microscopy The Lorentz force for an electron passin throuh a specimen with manetic field strenth (flux density) B v is iven by v v v F = e( B) where e is the electron chare and v v is the velocity of the electron. This is the same force which the microscope's manetic lenses use. The manetic deflection of an electron can be utilized to imae manetic domains. Like the manetic field of the lens, the field within a sample can deflect electrons, thus causin contrast in the imae. This phenomenon is the essence of Lorentz microscopy. Lorentz microscopy is a powerful technique for investiatin thin manetic films because it offers hih resolution, provides an unequivocal identification of the local manetization R. Ubic 30

31 direction, and permits correlations to be made between the manetic structure and the underlyin crystalloraphic structure of the film. The techniques which utilise the microscope in this mode include Fresnel and Foucault imain as well as differential phase contrast (DPC) imain with semented detectors in a STEM. Due to the necessity of imain manetic materials in a fieldfree reion to prevent manetization saturation, the spatial resolution of these techniques has historically been restricted to 10nm or more. In practice, in order to use any of these methods, it is important to remove the manetic field around the sample by shuttin off the objective lens. For this reason, Lorentz microscopy can only be done in LOW MAG mode in the microscope. It may also be useful to use the manetic field cancellin device, which deausses the objective lens, before startin. a. Fresnel imain Lorentz out-of-focus (Fresnel) microscopy has limited applicability for ultrathin layers because of overlappin contrast due to Fresnel frines; however, it does produce some very useful imaes. To imae in this mode, it is first necessary to focus an imae in LOW MAG mode, then chane the focus a lot. This over/under focusin both produces the Lorentz contrast but simultaneously derades resolution. When a defocused beam encounters the manetic field in one manetic domain, it is deflected, as shown above. The beam which hits the adjacent domain will be deflected oppositely. These deflections result in some beams overlappin, creatin a briht line in the imae, whilst others are kept apart, resultin in a dark line in the imae. The nearer to focus the imae is, the less Lorentz contrast there will be; at focus, there is no contrast. R. Ubic 31

32 If no manetic structure is visible, it is possible to induce one by tiltin or turnin on the objective lens current very slihtly usin the Free Lens Control (FLC). Tiltin the specimen reorients its manetic dipoles so that they have a reater chance of interactin with electron beam. Increasin the OL current can also force the formation of manetic domains. b. Foucault imain selected-area aperture In Foucault imain, focus is maintained, so resolution is better than in Fresnel imain. In order to operate in Foucault mode, it is necessary to first insert an objective aperture. Find a jo in the aperture imae and focus the beam (o to crossover). Then, increase the manification of the aperture but not the imae usin the Brihtness knob. The crossover point can then be moved to the selected area aperture (SA) with the Brihtness knob (manification should be at least 500X). The intermediate lens (IL) can be used to focus, and the objective minilens (OM) to chane the field. The SA can then be used to select deflected rays from one domain or the other - or both - as shown above. R. Ubic 3

33 c. Hih dispersion diffraction It is possible to obtain a diffraction pattern from a manetic sample in order to verify the number of domains present. A small condenser aperture is inserted, and the FLC is used to turn off all the lenses below CL3. In this set-up, the microscope behaves like an electron diffraction camera. Each spot which appears is the transmitted (000) spot from a different manetic domain. The separation between spots is a function of the sample thickness and the manetic saturation (M sat ). R. Ubic 33