Chapter 11 TEM imaging of crystal defects. Robin Schäublin CRPP-EPFL.

Transcription

1 Chapter 11 TEM imaging of crystal defects Robin Schäublin CRPP-EPFL 1. Introduction! 1.1 Motivation 2.! 2.1 Origin of contrast! 2.2 g.b analysis! 2.3 Weak-beam technique 3. Transmission Electron Microscopy imaging! 3.1 Image simulations!! TEM imaging of defects!! Simulation techniques (many beam, multislice)! 3.2 Applications!! Dislocation splitting!! Dislocation loops!! Stacking fault tetrahedra 4. Positron Annihilation Spectroscopy 5. Small Angle Neutron Scattering

2 Introduction Defects 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 defects The dislocation Dislocation 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).

3 ITER (International Thermonuclear Experimental Reactor) Operational in 2020 Q " 10 Fusion power: 500 MW Cost: 5 billion US$ Promises of the fusion reactor: Long term, sustainable and economic energy source. Safe (no risk of a nuclear accident as for fission reactors). Minimal long lived radioactive products. Possible recycling of structural materials, lithium coolant, unburned or burned fuel. The displacement cascade Production of: Interstitials Vacancies Impurities Clusters of interstitials, vacancies and impurities légende : atome de la cible interstitiel lacune impureté

4 Irradiation 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 transmutation Tensile test of single crystal Ni Tensile test of F/M steel F82H Effect on the plasticity Single crystal pure Ni, unirradiated Deformed in uniaxial tension at 5x10-5 s -1 Traction axis: <110> Test duration: 3.5 hours, elongation: ~120 %

5 Single crystal pure Ni, irradiated to 0.1 dpa at room temperature Deformed in uniaxial tension at 1x10-4 s -1 Traction axis: <110> Test duration: 2 hours, elongation: ~120 % Resulting microstructure: 100 nm 10 nm 25 nm

6 Deformation proceeds by flow localization or defect free channels Channels appearing in deformed irradiated single crystal pure Ni Channel crossing a grain boundary in irradiated polycristalline Fe-12Cr Hardening: #! = " # b [Nd] 1/2 Need for accuracy in the determination of: Defect density (N) Defect size (d) Obstacle strength (") Works in pure fcc metals Does not work in bcc Fe and F/M steels Difficulty in TEM resides in the size of the radiation induced damage that is at the limit of the TEM resolution (about 1 nm). -> Need for good TEM observations and image matching to simulations

7 Fe edge dislocation 2 nm void 10 K fcc Cu, irradiated, deformed in-situ, TV camera

8 fcc Cu, irradiated, deformed in-situ, CCD camera fcc Cu, irradiated, deformed in-situ at 183 K, CCD camera The string

9 The Utterly Butterly aerobatic team perform at the Zhuhai Airshow 2004 in southern China. US pair, Melissa Gregory and Denis Petukhov, perform during the Ice Dance 2004 original dance in Nagoya, Japan. Image interpretation problem... Experiments Modelisation e.g. Stacking fault tetrahedra in irradiated copper? TEM and material defects Simulations 2 nm 50 nm Cu 0.01 dpa RT weak beam g(6g) g = (200) Molecular dynamics simulation Pair potential method, atoms

10 1. Introduction! 1.1 Motivation 2.! 2.1 Origin of contrast! 2.2 g.b analysis! 2.3 Weak-beam technique 3. Transmission Electron Microscopy imaging! 3.1 Image simulations!! TEM imaging of defects!! Simulation techniques (many beam, multislice)! 3.2 Applications!! Dislocation splitting!! Dislocation loops!! Stacking fault tetrahedra 4. Positron Annihilation Spectroscopy 5. Small Angle Neutron Scattering Electrons Sample! 1.1 Motivation 37-interstitial Frank loop in Al Objective lens Objective aperture Film 2 nm High Resolution imaging mode Diffraction contrast imaging mode

11 Ewald construction beam direction:!! + g + Sg " 0 " 1 " 4 -g 0 g 2g 3g 4g 5g Sg Ewald sphere Sg: deviation parameter systematic row Crystal 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. Diffraction condition

12 Dislocation in crystal Perfect crystal Intensity profile Distorted crystal Real position Image position? Dislocation Burgers vector? Dislocation image position? g.b analysis Defect sizing, dissociation width, nature g.b analysis g perpendicular to b dislocation invisible, g.b = 0 b 3 unknowns 3 equations In practice: Minimum 4 different g, non-coplanar Edge component give residual contrast Complete extinction only when g.b x u = 0 Best g? Sharp, thin dislocation contrast

13 BCC crystal orientation map (01-1) (21-1) (200) (01-1) [133] [122] 5 [011] (-12-1) (12-1) (-200) [023] [012] (03-1) [013] (-200) [123] (10-1) [233] [111] [223] [112] (1-10) (22-2) [113] (1-10) (12-1) (21-1) (1-10) [001] 5 5 (020) (110) (200) FCC crystal orientation map (-11-1) (11-1) (200) (02-2) [133] [122] 5 [011] (04-2) (2-20) [023] (-200) [012] (-13-1) (13-1) [013] (-200) [123] [112] (11-1) [113] (24-2) (2-20) (2-20) 5 5 (020) (220) (200) [111] [223] (42-2) [001] (20-2) [233]

14 [10-10] HCP crystal [5-1-40] orientation map 10 [2-1-10] [7-2-53] [2-1-11] [10-11] [4-2-23] [5-1-46] [2-1-12] index 3 index Direction: [u,v,t,w] [U,V,W] Plane: (h,k,i,l) (H,K,L) From 4 to 3: U = u-t H = h V = v-t K = k W = w L = l h + k = -i and u + v = -t From 3 to 4: u = 2/3*U-1/3*V h = H v = 2/3*V-1/3*U k = K t =-1/3*V-1/3*U i = -(H+K) w = W l = L [2-1-13] [10-12] [4-2-29] [10-13] [2-1-16] [2-1-19] [0001] Dislocation density Unit of m -2 Number of intersections N with dislocations made by random straight lines of length L Density = 2 N / L t (t : foil thickness) Problems: Dislocations lost during sample preparation Overlapping of dislocations For a given family of dislocation (same type of b, e.g. 1/2{110}) some can be invisible: hkl Proportion of invisible disloc / / / / / / /6 420 all visible

15 Contrast of a dislocation loop Interstitial or vacancy nature of the loop? Inside-outside contrast analysis Contrast of a dislocation loop Analysis depends on size d of the loop: d > 50 nm same as for dislocations 10 nm < d < 50 nm Inside/outside contrast analyis (coffee bean contrast) d < 10 nm g.b analysis (black/white contrast): Black/white contrast reverses with defect depth Determination of defect depth and sense of black/white contrast 2 1/2 D technique (Mitchel and Bell)

16 Weak beam technique Extinction distance: Effective extinction dislocation: Parameter w: Weak beam technique (Cockayne, Ray and Whelan 1969) For copper, 100 kv: s g > 0.2 nm -1 ensures a single image per dislocation or partial dislocation Image position of dislocation is given by: The turning point Dislocation contrast width:

17 1. Introduction! 1.1 Motivation 2.! 2.1 Origin of contrast! 2.2 g.b analysis! 2.3 Weak-beam technique 3. Transmission Electron Microscopy imaging! 3.1 Image simulations!! TEM imaging of defects!! Simulation techniques (many beam, multislice)! 3.2 Applications!! Dislocation splitting!! Dislocation loops!! Stacking fault tetrahedra 4. Positron Annihilation Spectroscopy 5. Small Angle Neutron Scattering TEM image simulations Every 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 contrast,! Structure 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?

18 Electrons Sample 37-interstitial Frank loop in Al Objective lens Objective aperture Film 2 nm High Resolution imaging mode Diffraction contrast imaging mode beam direction:!! + g + Sg " 0 " 1 " 4 -g 0 g 2g 3g 4g 5g Sg Ewald sphere Sg: deviation parameter systematic row Crystal 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.

19 TEM image simulations There are two main types of simulation techniques: 1) Many beam calculation 2) Multislice calculation The many beam calculation originates from the calculation of intensities of X-Ray diffraction (1930 s). 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 and 2) 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. Many beam calculation -> Howie-Whelan equations for two beams A 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: " V(r) = h2 U g exp (- 2!i gr(r)) exp (2! i gr) 2 m e g 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 Schrödinger's wave equation is:! 2 "(r) + ( 8! 2 m e h 2 ) E + V(r) "(r ) = 0 %(r) is the function associated to the electron wave that moves through the faulted crystal. The proposed solution to the Schrödinger equation is: "!(r ) = " g exp (2! i (# + g + s g )r ) g 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).

20 Many beam calculation We will take a co-ordinate 'g along every beam direction. We then substitute V(r) and %(r) in the Schrödinger equation. We obtain a system of n differential equations of the first order with n unknowns &g(r):!! g (r)!" g # # h " i $ g-h! h (r) exp (2" i (h- g)r(r) + 2"i (s h - s 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 approximation!!" g # d dz The column approximation means that we consider only the direction of the transmitted beam to make the integration; so that: Many beam calculation We can then write the equation system in a matrix form: d!(r ) = M!(r ) where:!(r) = dz " 0 " 1 " n The matrix M is symmetrical and has the following expression: A A 1 Ai An A B Ai... An Cij Bi Cij Bn

21 Many beam calculation Where the coefficients are: A = -! 1! 0 ' A i = i! 1 1! i + i! i ' B i = -! 1! 0 ' + 2i s i! 1 + 2!i d dz g i R(r) C ij = i! i '! i-j! i-j (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. Many beam calculation We use relation (6) to compute d&o(r)/dz: d! 0 = - " 1! i " i dz ' " 0 " ' i " i! i + +i " 1 1 " n + i " n '! n The general equation for a d&i(r)/dz is: d! k dz =i " i! i " i " ' i " i " ' i-j " i-j + - " 1 " 0 '! j + + 2i s i " 1 + 2!i d dz g i R(r)! i + +i " i " ' i-n " i-n! n 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).

22 Many beam calculation References C.T. Forwood and L.M. Clarebrough, Electron Microscopy of Interfaces in Metals and Alloys, Adam Hilger Ed., Bristol, Philadelphia and New York, 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, Amsterdam, P.B. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley and M.J. Whelan, Electron Microscopy of Thin Crystals, London, R. and P. Stadelmann, "A method for simulating electron microscope dislocation images", Materials Science and Engineering, A 164 (1993) P.A. Stadelmann, "EMS A software package for electron diffraction analysis and HREM image simulation in materials science", Ultramicroscopy, 21 (1987) A. Weickenmeier and H. Kohl, Acta Cryst. A47 (1991) 590. Many beam calculation Data required to make an image simulation: Material:! Space group,! Lattice parameter,! Atomic positions,! Elastic constants (unit:1012 dyne/cm2) Geometry (based on the Head et al. program, dimension unit: nm):! Foil normal,! Electron beam direction,! Dislocation line direction,! Burgers vector for each dislocation, set to 1/1[0,0,0] if no dislocation,! Fault plane normal (plane related by adjacent dislocations), set to [0,0,0] if no plane,! Lattice translation vector (in the above mentioned plane), set to 1/1[0,0,0] if no fault on plane,! Width of plane,! Thickness of the thin foil. Diffraction condition:! Acceleration voltage,! When you have a weak beam condition (e.g. g=[002], g(4g)) the diffraction condition is described by:!! One diffraction vector (g=[002]),!! The vector describing the projection of the Ewald sphere center on the systematic row (2g=[004]),!! (centre of the Laue circle)! If you have additional diffraction spots (out of the systematic row), describe! them as follows:!! Diffraction vector,!! Deviation parameter.

23 Many beam calculation e - e - "Generalised "Generalised cross-section" cross-section" thin foil with one dislocation thin foil with two dislocations and a planar fault image image Many beam calculation Simulated "-fringes, attributed to segregation, bordered by a 1/2[-1,-1,0] dislocation in )' precipitate of a Ni3(Al,Ta) superalloy. Lattice translation: 1/10[0,1,0]. Scale bar is 100 nm.

24 Comparison of simulated and experimental images of dislocation loops in Mo edge loops! Simulations based on Howie-Whelan equations (or their equivalent).! Harwell code 2-beam.! Dynamical imaging conditions (s g = 0). English, Eyre and Holmes, 1980 Bright-field kinematical vs weak-beam Down-zone Weak-beam Copper irradiated with 600keV Cu + ions

25 Stacking-fault tetrahedra in quenched gold! nm Defects with complex geometry in ionirradiated silver

26 For very small defects, weak-beam contrast varies with s g What about the column approximation? Non-column approximation formulation: Theory: the Howie-Basinski equations Imperfect crystal Bloch wave theorem + Non-column approximation is possible but more complex to integrate numerically

27 The column approximation and many-beam effects g = 002 5nm edge-on Frank loop Experimental (g,1.0g) (g,3.75g) (g,4.75g) (g,6.25g) Many-beams, non-ca Many-beam, CA Two-beam, non-ca The column approximation (CA) is, in some particular cases, not appropriate Multislice technique *(r)j = [*(r)j-1 qj] x pj->j+1 *(r)j : Wave function entering slice j+1, qj : Function of the transmittance of the slice j, pj->j+1 : Function of propagation (propagator) from slice j to slice j+1. Reference: J.M. Cowley, A.F. Moodie, Acta Cryst. 10 (1957) 609.

28 Multislice technique Data required to make an image simulation: Material:! Atomic positions (no limit in the number of atoms!) Diffraction condition:! Acceleration voltage That is all! Question: How to define the diffraction condition? Multislice technique The beam direction is defined by the normal to the slices. This implies in most of the cases of molecular dynamics simulation that the beam direction is a low index crystallographic direction such as <001>, <011>, <111> or at most <112>: -> Appropriate for HREM and atomic imaging. -> Not approprate for CTEM imaging. For CTEM it is more appropriate to image with a single systematic row, defined by one diffraction vector g. In order to attain such an imaging condition, a method was developed. It consists in tilting the specimen before slicing. This corresponds in fact to what the operator is doing on the microscope. The idea is to go away from the main zone axes, by about 10, by a first tilt around the diffraction vector that will define the systematic row. To reach the desired weak beam condition, such as g(4g) it is still necessary to do a second tilt, perpendicular to the diffraction vector, of about 1.

29 Multislice technique Defining the diffraction condition First tilt: Multislice technique Defining the diffraction condition Being based on (fast) Fourier transforms, the multislice technique requires periodic slices in x and y. Otherwise artificial contrasts entre in the image from the boundaries of the image, as if they were planar faults at the boundaries. While this condition is preserved in molecular dynamics samples calculated with periodic boundary conditions, this is not true anymore when this same specimen is tilted before slicing. -> Slicing direction is selected in order to perserve periodicity, e.g. from [001] to [015]:

30 Multislice technique Defining the diffraction condition Second tilt: The second tilt is performed by shifting the slices by some $x at every slice. This approximation is based on the fact that in each slice atomic positions, or scattering centres, are projected onto a 2D representation. The resulting projected potential is insensitive to differences in height of the atoms within one slice. The horizontal position however is slightly affected by a real tilt, but the difference is negligleable for angles in the 1 range. Multislice technique Considerations on sample size and sampling Sampling should allow for sufficient spatial resolution. It appears that a pixel size of about 0.1 Angstroem is sufficient. In practice this implies that to simulate the image of a molecular dynamics sample of, for example, Al atoms in a cube, a sampling of 1024x1024 is appropriate. This results in a square image that is about 10 nm a side (with hence a spatial resolution of about 0.1 Angstroem). Calculation time is also something to consider. The above example is calculated nowadays in about 1 day in a single processor machine. When a higher number of atoms is treated the calculation time increases for two reasons. The first is due to the calculation of the interaction of the electron wave with a larger number of scattering centres, and the second is due to the higher sampling, e.g. 2048x2048 or higher, needed because of the larger MD box. 3 to 4 millions atoms are nowadays manageable, including both the image simulation time and the handling of the image in image treatment softwares (PhotoShop or other). This represents a cubic box with side of 40 nm, which is quite close to what is handled experimentally in a TEM, both in terms of sample thickness and image area. Simulation techniques: many beam calculation or multislice technique Both have advantages and drawbacks, one has to carefully design the project before jumping onto them: Many beam calculation: complex data set, easy to run and fast Multislice technique: easy data set, complex to run and slow

31 1. Introduction! 1.1 Motivation 2.! 2.1 Origin of contrast! 2.2 g.b analysis! 2.3 Weak-beam technique 3. Transmission Electron Microscopy imaging! 3.1 Image simulations!! TEM imaging of defects!! Simulation techniques (many beam, multislice)! 3.2 Applications!! Dislocation splitting!! Dislocation loops!! Stacking fault tetrahedra 4. Positron Annihilation Spectroscopy 5. Small Angle Neutron Scattering g(2.5g) g(2.8g) (a) 0.0 mrad (b) (c) mrad Number mrad 3 mrad 5 mrad Effect of beam convergence g(3.0g) 1.0 mrad Apparent separation [nm] 6.0 g(3.3g) 3.0 mrad 3.0 (d) g(3.5g) 10 nm 5.0 mrad 10.0 mrad 10 nm Apparent separation [nm] Beam convergence [mrad] 10 Simulated WB-TEM images of a screw dislocation in Cu (a) (parallel beam) as a function of deviation, and (b) (g(3.1g) condition) as a function of convergence. (c) Histogram of # values measured locally and (d) average # as a function of convergence. Improvement of the measurement by including convergence (deduced from sim!)

32 0.0 mrad! 0.5 mrad! 1.0 mrad! 3.0 mrad! 5.0 mrad g(2.8)g g(2.9)g g(3.0)g g(3.1)g Table of simulated WB-TEM images of a screw dislocation in a wedge sample showing the contrast evolution as a function of deviation (left side scale) and convergence (top scale). The wedge sample thickness ranges from 0 to 200%nm. To show changes in contrast between images the intensities are logarithmic and are scaled differently. g(3.2)g g(3.3)g 5 nm 50 nm Experimental application: The case of the 30 dislocation in Ni3Al g Character Beam Normal Foil Normal Sg b partial Thickness nm -1 1/2[101 - ] 76nm X. Meng 1mrad 5mrad Experiment-1 mrad Experiment-4.5mrad Position of highly excited diffration spot in g unit

33 A value of 183±8%erg/cm 2 ( apparent partial spacing #= 3.47 ± 0.15 nm) is obtained for the APB energy in Ni3Al. Experiment Simulation Exp-Time Spacing! Spacing 2.8 s 3.47 nm 4.5 mrad 3.51 nm 22 s 3.59 nm 1 mrad 3.53 nm Improvement of the measurement by including beam convergence The Frank loop-type cluster in Al Interstitial Frank loop simulated TEM images using weak beam g(3.1g), g=(200) at 200 kv in Al for a diameter of about (a) 1.0 nm (8 interstitials), (b) 1.5 nm (19 interstitials) and (c) 2.0 nm (37 interstitials). Simulations indicate that nanometric loop size is difficult to resolve below 2 nm

34 Evolution of the TEM contrast of the dislocation loop with size Simulations indicate that nanometric loop image size saturates < 1 nm Simulations indicate that a cluster of 2 interstitials has 20 % contrast, enough to be seen experimentally, in principle! (background noise is in general 10%) Large loops MD simulation Jaime Marian LLNL USA Interstitial loop in pure Fe 937 interstitial <100> loop on (100) plane Weak beam g(4.1g) g=(200) 200 kv thickness 18 nm Image width = 22.9 nm Good match between experimental and simulated image of dislocation loop in steel Allows raising ambiguity on the identification of the loop s Burgers vector

35 SFT in fcc metals TEM weak beam images in Cu, Ni and Pd irradiated at room temperature and at a dose of, respectively, dpa, %dpa and dpa. Diffraction condition is g={200}, g(6g), about 10 off <011>. Simulations could help identifying SFT? Stacking fault tetrahedra in irradiated copper TEM and material defects Experiments Simulations 2 nm 50 nm Cu 0.01 dpa RT weak beam g(6g) g = (200) Molecular dynamics simulation Pair potential method, atoms Simulations allow closing the gap between experiments and simulations

36 a b c d e f g h i 2 nm SFT simulated TEM images using weak beam g(6.1g), g=(200) at 200 kv in Cu as a func - tion of SFT size and sample thickness. 21-vacancies SFT in a sample (a) 10.4 nm, (b) 11.6 nm and (c) 13.2 nm thick. 45-vacancies SFT in a sample (d) 13.6 nm, (e) 12.0 nm and (f) 15.2 nm thick. 91-vacancies SFT in a sample (g) 10.4 nm, (h) 11.6 nm and (i) 13.2 nm thick. Simulations indicate that SFT s contrast in TEM is more complex that one generally assumes (contrast changes from white to black! SFTs below 2 nm look like loops!) Table of TEM weak beam images in Cu irradiated at room temperature to dpa, showing (row a) perfect SFTs, (row b) truncated SFTs and (row c) groups of intermixed SFT. First column of images (a, b and c) shows corresponding simulated images while second to fourth columns (a1-a4, b1-b4 and c1-c4) show corresponding typical experimental images of those. Simulations indicate that nanometric loop size is difficult to resolve below 2 nm

37 M. J. Caturla, Univ. of Alicante MD simulated 10 kev cascade in Al MD sample: projection of vacancies (light symbol) and interstitials (dark symbol) on the plane of the TEM picture ([015] projection). Simulated weak beam image, with g(3.1g), g=(200), 200 kv.

38 TEM investigation of cavities in irradiated F/M steel (F82H) Fresnel imaging based on the defocusing technique: Cavities appear as bright disks surrounded by a dark ring, or vice-versa, depending on defocus value.

39 Simulated TEM images of MD simulated cavities in Al. Fresnel contrast is visible on the simulated kinematical bright field, either underfocused (middle image) or overfocused (right image). STEM approach (1) 2 Å probe scanned over the surface, signal on annular detector Simulations based on multislice technique (Kirkland code)

40 STEM approach (2) High contrast, high resolution. Resolution degrades with thickness. STEM approach is promising in the analysis of nanometric defects Better acquisition system (in time resolution, CCD camera) Better optics: new objective aperture? ø20 µm ø40 µm 50x100 µm2 Rectangular aperture: gain in resolution (6.5 Å down to 3.0 Å, theoretical)

41 1. Introduction! 1.1 Motivation 2.! 2.1 Origin of contrast! 2.2 g.b analysis! 2.3 Weak-beam technique 3. Transmission Electron Microscopy imaging! 3.1 Image simulations!! TEM imaging of defects!! Simulation techniques (many beam, multislice)! 3.2 Applications!! Dislocation splitting!! Dislocation loops!! Stacking fault tetrahedra 4. Positron Annihilation Spectroscopy 5. Small Angle Neutron Scattering Positron annihilation spectroscopy Allows the detection of cavities in materials. Positron are naturally emitted by some radioisotopes as a result of their decay. Positron annihilates with 1 electron according to: 1 e e - > 2 photons (511 kev each) Its life time depends on its environment. In materials it is usually of the order of 1 ns.

42 Positron annihilation spectroscopy Gamma Detector Radioactive source ( 22 Na usually) Gamma Detector Sample Time resolved coincidence detector Reference time is given by the detection of a 1.28 MeV gamma ray, emitted at the same time as the positron. Thermalization of the positron in about 10 ps Positron travels about 100 nm Cu: Annihilation time in the bulk: 110 ps (trapping rate: s -1 ) Annihilation time with single vacancies: 175 ps (trapping rate: s -1 ) 1 ppm vacancies > 10% trapped Density resolution: Lower limit: 0.1 ppm Upper limit: 100 ppm

43 Size resolution: Depends on the annihilation time difference between the different cavity populations. Should be > 50 % In practice: 3 populations at maximum are resolved Smaller size: 1 vacancy (annihilation time 175 ps) Larger size: vacancies (annihilation time 500 ps) e - e + Small cavity Large cavity & inner surface for positron > saturation in trapping ability Positron annihilation spectroscopy Simulated positron density in a (a) perfect crystal and (b) a crystal with a vacancy Richard H. Howell et al., "Positron Beam Lifetime Spectroscopy at Lawrence Livermore National Laboratory," Application of Accelerators in Research and Industry, J. L. Duggan and I. L. Morgan, Eds., New York: AIP Press, 1997

44 Evidence for microvoids in irradiated F82H Size & 1-2 nm Fe: M. Eldrup, B.N. Singh, Journal of Nuclear Materials 276 (2000) Positron annihilation spectroscopy Other sources: Accelerated positrons, either from a classical source ( 22 Na) or from pair production (e -, e + ) in a target. Pelletron at LLNL, allows for sample thickness up to centimetres

45 1. Introduction! 1.1 Motivation 2.! 2.1 Origin of contrast! 2.2 g.b analysis! 2.3 Weak-beam technique 3. Transmission Electron Microscopy imaging! 3.1 Image simulations!! TEM imaging of defects!! Simulation techniques (many beam, multislice)! 3.2 Applications!! Dislocation splitting!! Dislocation loops!! Stacking fault tetrahedra 4. Positron Annihilation Spectroscopy 5. Small Angle Neutron Scattering Neutron scattering Two different interactions between a neutron and atoms in a crystal exist: 1) Nuclear interaction : neutron-atom nuclei interaction 2) Magnetic interaction : Neutron magnetic moment - atom magnetic moment

46 Normalised atomic scattering factors for iron. 512x512 pixels EUROFER97 1dpa 350 C

47 512x512 pixels Water (H 2 O) 1 I(Q) (arbitrary unit) dpa 1.47 dpa 0 dpa Q(nm -1 ) Scattering intensity in arbitrary units versus scattering vectors for unirradiated and irradiated specimens of F82H

48 0.03 N(R) ( arbitrary unit) dpa 1.47 dpa R(nm) Size distribution of scattering objects in irradiated F82H for two different doses SANS analysis Neutron wavelength +: 0.5 nm Sample-detector distance: 2 m (128x128 pixel detector) > The scattering vector Q ranges from 0.3 to 3 nm -1 (Q = 4'sin,/+, 2, is the scattering angle)

49 Comparing TEM and SANS TEM Resolution limit: ~1 nm (limited by obj. apert. size, note: wavelength is ~2.5 pm) very sensitive to displacement fields little sensitive to cavities Probes ~µm 3 Direct observation of individual defects Bad statistics SANS resolution limit: ~0.5 nm (limited by wavelength) little sensitive to displacement fields very sensitive to cavities, in particular in magnetic field Probes ~mm 3 Signal fitted to a given type and size distribution of defects Good statistics Range of application of different techniques Defect Size Resolved defect size [m] 10-2 SEM/STM/AFM TEM OM X-Ray SANS PAS Sample thickness, depth [m]

50 Range of application of different techniques Defect Concentration Resolved defect concetration [m -3 ] 10-1 SEM/STM/AFM TEM PAS X-Ray SANS Sample thickness, depth [m] Thank you for your attention and best wishes for your future