ABSTRACT
Abstract ................................................................................................. 490 5.1 Introduction .................................................................................. 491 5.2 X-Ray Diffraction Applied To Crystalline Systems..................... 493 5.2.1 X-Ray and Diffraction on Crystals ................................... 493 5.2.2 X-ray and the Electronic Density ..................................... 503 5.2.3 The Ewald X-Rays Diffraction Rationalization ................511 5.2.4 X-Ray and Structure Determination ................................. 521 5.3 Fields and Intensities in Dynamical Theory of
X-Ray Diffraction ........................................................................ 533 5.3.1 Fundamental Equations .................................................... 533 5.3.2 Dynamical Diffraction in Two Waves Approximation ..... 538 5.3.3 The Case of Zero Absorption ........................................... 544 5.3.3.1 The Thick Crystal Case ..................................... 547 5.3.3.2 The Thin Crystal Case ...................................... 549 5.3.3.3 The Case of Intermediate Thickness Crystal .... 550 5.3.4 The Case of the Crystals with Absorption ........................ 554 5.4 Pendellösung Phenomena: The Plane Waves Approximations .... 561 5.4.1 The Phenomenology of Ewald’s Pendellösung ................ 561 5.4.2 Analytical Ewald’s Pendellösung ..................................... 564 5.4.2.1 The Coupling of Poynting Vectors .................... 565 5.4.2.2 Direction of Propagation of Poynting Vectors .. 570 5.4.3 Integrated Intensities over the Pendellösung Period:
The Laue’s Case ............................................................... 574
5.4.4 Electronic Density by Structure Factor for Deformed Crystals ........................................................... 581
5.4.4.1 Pendellösung and the Electronic Ordered Structure .............................................. 581
5.4.4.2 Modeling of Elastic Deformation of the Crystalline Structure ......................................... 582
5.4.4.3 Pendellösung and the Amplitude of the Structure Factor ................................................. 584
5.4.4.4 Application to the Electronic Maps of Contour ......................................................... 589
5.5 Total Self-Consistency in X-Ray Diffraction ............................... 596 5.5.1 Borrmann Phenomenology ............................................... 596 5.5.2 Quantum Modeling of Dynamical Bormann Effect ......... 599 5.5.2.1 Formulation of Quantum State Vectors............. 599 5.5.2.2 Quantum Dynamic Localization ....................... 601 5.5.2.3 The Quantum Diffracted Energies .................... 606 5.5.2.4 The Quantum Dynamic Jump ........................... 610 5.6 Conclusion ................................................................................... 615 Keywords .............................................................................................. 617 References ............................................................................................. 617 Author’s Main References ........................................................... 617 Specific References ...................................................................... 618 Further Readings .......................................................................... 621
ABSTRACT
The journey toward the depths of the structure of condensed state will eventually proceed through an “external non-destructive intervention”, with the aid of the X-radiations on the crystals; we should note that X-rays interact with the electrons of the atoms or the groups of atoms from the network and not with their nuclei. Thus, the picture of diffraction (reflection or scattering) of the X-ray will generate an “electronic map” of the bodies investigated, so characterizing their structure. Moreover, this
electronic map is a manifestation of the so-called structure factor of the crystal analyzed a quantity in direct (Fourier) relationship with the associated electronic density. This way, the union between the experimental methods with X-ray diffraction on crystals and their quantum characterization is so retrieved by means of the electronic densities characteristic to the structures. Practical ways of refining of this merging between crystals and X-ray diffraction are the main focus of the present chapter.
