Electron Microscopy Images of Rectilinear Dislocations Crossing the Surface at an Arbitrary Angle

Филиппов, А. П.; Gaidukov, G. N.; Maksimov, S. K.

doi:10.1002/pssa.2210940105

Cited by 6 publications

(7 citation statements)

References 7 publications

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“…Numerical analyses involve the identification of the geometry of the dislocations in a thin foil (e.g. TEMPACK [13]), calculations of theoretical two-beam images without [14][15] or with the assumption of free surface relaxation [16,17]. In addition, for the interpretation of HRTEM images, appropriate numerical tools have been utilised (EMS [18], HRPACK [19]) to simulate the elastic displacement field of atom columns around the dislocation cores, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Crystalline Defects in a B.C.T. Al2Cu(?) Single Crystal Obtained by Unidirectional Solidification along [001]

Bonnet

Loubradou

2002

phys. stat. sol. (a)

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A directionally solidified Al2Cu(θ) crystal (body centred tetragonal lattice, a = 0.6063 nm, c = 0.4872 nm) grown along the c axis has been observed by transmission electron microscopy (TEM) to investigate the solidification defects. In a first step, using two‐beam TEM, matrix dislocations with large Burgers vectors 1/2〈111〉, [001], and [100] were positively identified, as well as a rectangular spiral source with a Burgers vector b = 1/2[$ \bar 1 \bar 1 \bar 1 $] acting along the ($ \bar 1 \bar 1 $2) plane. These defects were identified from the comparison between sets of experimental and theoretical images. It is shown that the topological contrasts of these dislocations can be highly affected by the elastic relaxation at both free surfaces of the thin foil. In a second step, a (110) facetted low angle tilt boundary with the c axis has been investigated by high resolution TEM. Its structure can be described as a succession of two consecutive mixed dislocations b = 1/2[111] and 1/2[11$ \bar 1 $], which gives for the pair an edge resultant Burgers vector [110]. A quite unusual core splitting is observed for one of these mixed dislocations since narrow faults extend on the (110) boundary plane. Around this complex core, the relative positions of the partials have been carefully determined at a near atomic scale using a dedicated simulation program using anisotropic elasticity theory. Large planar faults along (001) are also sometimes noticed. These results stress that, in the characterisation of crystalline defects in crystals with large lattice parameters, numerical methods provide an important advantage over classical methods based on qualitative arguments only.

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Section: Introductionmentioning

confidence: 99%

Crystalline Defects in a B.C.T. Al2Cu(?) Single Crystal Obtained by Unidirectional Solidification along [001]

Bonnet

Loubradou

2002

phys. stat. sol. (a)

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“…Therefore, computed TEM micrographs of a biperiodic network of MDs are now possible in a manner similar ot that used by Filippov et al [7] or Humble [37] for simulating the contrast of straight matrix dislocations emerging to the free surface of a semi-infinite isotropic crystal. Note also that the present analytical approach may be applied to configurations involving dissociations of the MDs in the interface plane.…”

Section: Discussionmentioning

confidence: 99%

“…Indeed, in [33], several geometries of dissociated hexagonal nodes were fully taken into account by other specific Fourier coefficients in Eq. (7).…”

Section: Discussionmentioning

confidence: 99%

A Biperiodic Network of Misfit Dislocations in a Thin Bicrystalline Foil

Bonnet¹

2000

phys. stat. sol. (a)

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The elastic displacement field u associated with a planar, periodic, hexagonal-based network extended parallel to the two free surfaces of an ultrathin foil is investigated when the material is a bicrystal formed by two different isotropic crystals. The geometry of the network may include, in principle, different interfacial domains limited by straight or curved MD segments. An explicit formulation of each harmonic term is derived that depends explicitly on the isotropic elasticity coefficients and thickness of each phase. The key of the solution is the inversion of a system of 12 Â 12 linear equations with 12 complex unknowns that expresses the limiting boundary conditions. Applications are given for regular honeycomb networks of MDs in CoSi 2 /Si thin foils.

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“…The Eshelby twist is well known to make it possible to image end‐on screws by diffraction contrast (Tunstall et al ., ; Williams & Carter, ) even though

g \cdot b = 0

and

g \cdot b \times u = 0

are satisfied at the same time. As a simple approximation, TEM diffraction contrast images of dislocation emerging at the top free surfaces of isotropic foil were computed using the approximation of a single free surface (Yoffe, ; Shaibani & Hazzledine, ; Filippov et al ., ). A better approximation for treating free surfaces of thin foil assume that the foil is divided into two parts separated by the median plane and the elastic displacement field of each volume is that of a dislocation piercing the nearby free surface of a semi‐infinite isotropic medium (Humble, ; Bonnet & Loubradou, ).…”

Section: Introductionmentioning

confidence: 97%

TEM diffraction contrast images simulation of dislocations

Schaeublin

2019

Journal of Microscopy

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Summary For end‐on screw dislocations and inclined dislocations within thin transmission electron microscopy (TEM) foil, TEM diffraction contrast image is largely modified around piercing point due to free surface relaxation. Based on many‐beam Schaeublin–Stadelmann equations, TEM diffraction contrast images simulation of inclined dislocations within thin pure Fe TEM foil are performed and the difference between isotropic and anisotropic dislocation models are studied. Image force are superposed onto bulk elastic field of dislocation in thin foil, the elastic distortions nearby the two emerging points of a straight inclined dislocation located in an elastically isotropic/anisotropic thin foil are expressed as semianalytical solution in Fourier space, and the semianalytical image stress solutions in Fourier space are implemented into CUFOUR for studying free surface relaxation effect on TEM diffraction contrast of dislocation. Simulation results suggest that the diffraction contrast at the ends of dislocation is modified drastically by image forces, and effects of anisotropy cannot be neglected. Lay Description For end‐on screw dislocations and inclined dislocations within thin transmission electron microscopy (TEM) foil, TEM diffraction contrast image is largely modified around piercing point due to free surface relaxation. Based on many‐beam Schaeublin–Stadelmann equations, TEM diffraction contrast images simulation of inclined dislocations within thin pure Fe TEM foil are performed and the difference between isotropic and anisotropic dislocation models are studied. Image force are superposed onto bulk elastic field of dislocation in thin foil, the elastic distortions nearby the two emerging points of a straight inclined dislocation located in an elastically isotropic/anisotropic thin foil are expressed as semianalytical solution in Fourier space, and the semianalytical image stress solutions in Fourier space are implemented into CUFOUR for studying free surface relaxation effect on TEM diffraction contrast of dislocation. Simulation results suggest that the diffraction contrast at the ends of dislocation is modified drastically by image forces, and effects of anisotropy cannot be neglected.

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Electron Microscopy Images of Rectilinear Dislocations Crossing the Surface at an Arbitrary Angle

Cited by 6 publications

References 7 publications

Crystalline Defects in a B.C.T. Al2Cu(?) Single Crystal Obtained by Unidirectional Solidification along [001]

Crystalline Defects in a B.C.T. Al2Cu(?) Single Crystal Obtained by Unidirectional Solidification along [001]

A Biperiodic Network of Misfit Dislocations in a Thin Bicrystalline Foil

TEM diffraction contrast images simulation of dislocations

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