Kikuchi patterns in a high voltage electron microscope

Evidence of the breakdown of Frieders law in the Kikuchi patterns of tellurium crystals has been observed with a standard transmission electron microscope (TEM). These observations give a direct method of identifying enantiomorphously related phases in the TEM. An interpretation of the observed deviations from Frieders law is proposed on the basis of the model of Thomas & Humphreys [Phys. Status Solidi A (1970). 3, 599-6151 for Kikuchi patterns. The possible differences between the phases of the Fourier coefficients of the crystal potential and of the absorption potential have to be taken into account. Some light is thrown on the physical significance of the phenomenological parameters.

Section: Discussionsupporting

confidence: 60%

Section: Discussionmentioning

confidence: 99%

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Breakdown of Friedel's Law in the Kikuchi patterns of tellurium

Faivre¹,

Goff²

1979

“…As was pointed out by Hall (1970), Ishida (1970Ishida ( , 1971 and Chukhovskii, Alexanjan & Pinsker (1973), the contrast reversal of Kikuchi bands can be explained by means of absorption of inelastically scattered electrons. This procedure, however, does not conserve the total probability and leads to an exponential decrease of the scattered electron density (Thomas & Humphreys, 1970;Serneels, Van Roost & Knuyt, 1982). This result is at variance with experimental observation (Uyeda & Nonoyama, 1967, 1968 of the Kikuchi pattern in thick crystals (where the thickness is larger than the mean free path with respect to inelastic collisions).…”

Section: Introductionmentioning

confidence: 53%

Multiple scattering theory for fast electrons in single crystals and Kikuchi patterns

Dudarev¹,

Ryazanov²

1988

By solving the kinetic equation for the density matrix of fast electrons the intensity distribution of the diffuse background and the Kikuchi lines and bands is found. It is shown that the Kikuchi pattern contrast depends on the angle of deflection of the scattered particles and the crystal thickness. For a thin crystal the expressions obtained coincide with the usual results found in the single inelastic scattering approximation. The theory takes into account both the dynamical diffraction and multiple inelastic scattering of electrons and gives a simple interpretation of a variety of contrast effects observed in thick single crystals.

“…the Kikuchi lines and bands, have been discussed by various authors (Pfister, 1953;Kainuma, 1955;Takagi, 1958;Fujimoto & Kainuma, 1963;Gjonnes, 1966;Hall, 1970;Thomas & Humphreys, 1970;Ishida, 1971;Okamoto, Ichinokawa & Ohtsuki, 1971), and at present the absorption-independent diffraction effects observed from relatively thin crystals are well understood. In particular, qualitative explanations have been given for various effects observed in the narrow lines (Kambe, 1957;Gjonnes & Watanabe, 1966;Uyeda, 1968;Gjonnes & Hoier, 1969;Lally, Humphreys, Metherel & Fischer, 1972;Hoier, 1972 a,b).…”

Section: Introductionmentioning

confidence: 99%

Multiple scattering and dynamical effects in diffuse electron scattering

Høier¹

1973

In reality the neighbours move and roughly these movements can be classified as 'in-phase' and 'out-ofphase'. For 'in-phase' movement the potential function is effectively softened, the mode frequencies are lowered and the amplitudes increased. This is not compensated fully by the 'out-of-phase' motions which correspond to raised frequencies and smaller amplitudes.In the structures of benzene and sulphur the arrangement of neighbours is much more isotropic than in pyrene and phenanthrene. Comparison of the individual diagonal elements of T and L in the cases of benzene and sulphur shows no enormous discrepancy over and above a softening factor. However as the structure becomes increasingly anisotropic so the softening factor increases and detailed discrepancies appear.The most striking discrepancy is in the value of T22 for pyrene. In this crystal pairs of molecules related by the centre of inversion lie on parallel planes distant 3.5/~, front each other, and they are almost perpendicular to the b axis. The close approach of so many atoms along this direction causes the potential to be very hard and the Einstein model gives a very small value, T22=0.0098 A 2. The lattice-dynamical calculation yields a value of 0.0486 A 2, which is in good agreement with the experimental value of 0.0369/~2. These experimental values come from the constrained refinement of neutron diffraction data (see Pawley, 1972b), and show a satisfactory overall agreement with the Born-von KS.rmS.n calculation.Thus it is possible to make qualitative arguments and conclusions using the diagonal elements of T and L. However no such argument can be used for the offdiagonal elements, including the elements of S. These are determined by the finer aspects of the molecular packing, and thus our understanding of intermolecular forces cannot be furthered by simple Einstein-model calculations. In many ways therefore our result is disappointing, but at least we learn to avoid making an assumption which is superficially plausible but which has no physical justification. A many-beam dynamical theory for Bragg scattering effects in diffuse electron scattering is developed which takes multiple diffuse scattering into account. For non-absorbing crystals the theory is shown to include previoas theories for Kikuchi lines and bands; with absorption, a weaker dependence on the anomalous absorption parameters than in previous theories is found. The variations in symmetrical Kikuchi-band contrast are discussed, and the thickness dependence of the angular range with excess contrast is explained. For typical higher-order systematic lines the theory predicts contrast variations similar to the ones found for the band, i.e. characteristic thickness-dependent disappearance angles and angle-dependent disappearance thicknesses for the line contrast. The low band contrast observed from very thick specimens is found to be due to the reduced anomalous absorption associated with the higherorder diffuse scattering contributions. Calculated Kikuchi-band contrast due to multiple ...