Numerical solutions of the Lamm equation. II. Equilibrium sedimentation

Biopolymers ◽  
1966 ◽  
Vol 4 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Menachem Dishon ◽  
George H. Weiss ◽  
David A. Yphantis
Keyword(s):  
Numerical Solutions ◽  
Equilibrium Sedimentation ◽  
Lamm Equation

Numerical solutions of the Lamm equation. IV. Rotor slowing experiments

Biopolymers ◽  
1967 ◽  
Vol 5 (10) ◽  
pp. 1021-1028 ◽  
Author(s):  
Irwin H. Billick ◽  
Menachem Dishon ◽  
George H. Weiss ◽  
David A. Yphantis
Keyword(s):  
Numerical Solutions ◽  
Lamm Equation

NUMERICAL SOLUTIONS OF THE LAMM EQUATION. V. BAND CENTRIFUGATION

1969 ◽  
Vol 164 (1 Advances in U) ◽  
pp. 33-51 ◽  
Author(s):  
Menachem Dishon ◽  
George H. Weiss ◽  
David A. Yphantis
Keyword(s):  
Numerical Solutions ◽  
V Band ◽  
Lamm Equation

Numerical solutions of the Lamm equation. I. Numerical procedure

Biopolymers ◽  
1966 ◽  
Vol 4 (4) ◽  
pp. 449-455 ◽  
Author(s):  
Menachem Dishon ◽  
George H. Weiss ◽  
David A. Yphantis
Keyword(s):  
Numerical Solutions ◽  
Numerical Procedure ◽  
Lamm Equation

Numerical solutions of the Lamm equation. III. Velocity centrifugation

Biopolymers ◽  
1967 ◽  
Vol 5 (8) ◽  
pp. 697-713 ◽  
Author(s):  
Menachem Dishon ◽  
George H. Weiss ◽  
David A. Yphantis
Keyword(s):  
Numerical Solutions ◽  
Lamm Equation

Atomic Imaging of Crystals using Large-Angle Electron Scattering in STEM

1990 ◽  
Vol 48 (1) ◽  
pp. 74-75
Author(s):  
D.E. Jesson ◽  
S. J. Pennycook
Keyword(s):  
Wave Function ◽  
Electron Scattering ◽  
Numerical Solutions ◽  
Large Angle ◽  
Real Space ◽  
High Angle ◽  
Analytical Treatment ◽  
Order Zero ◽  
Experimental Conditions ◽  
Ewald Sphere

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;

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