X-ray Takagi-Taupin dynamical theory generalized to n-beam diffraction cases.
A new X-ray dynamical diffraction theory that can deal with n-beam cases comprehensively (n in [3, 4, 6, 8, 12]) has been derived based on the Takagi-Taupin dynamical theory. The new theory takes into account correctly the effects of arbitrarily polarized incident X-rays and the polarization states of X-ray wavefields in a crystal. Furthermore, an arbitrary lattice displacement in the crystal can be dealt with. The new theory has a high symmetry and therefore can be written with one equation supposing that suffixes are taken in 2n ways, where the suffixes indicate ordinal numbers of waves and polarization states. This simplicity of the theory enables a computer program to solve the equations to be coded easily. A method to solve the theory numerically is also described. 'Six-beam X-ray section topographs' computer simulated based on the new theory are also presented.
Statistical dynamical theory of crystal diffraction. II. Intensity distribution and integrated intensity in the Laue cases
The theory described in the previous paper [Kato (1980). Acta Cryst. A36, 763-769] has been applied to calculating the intensity distribution in the topography of statistically homogeneous crystalline media. The integrated intensity for parallel-sided crystals is also presented. The formulae cover the whole range of crystal perfection. Primary and secondary extinctions can be treated on a unified theoretical base. A few numerical examples are given to demonstrate the variations of the integrated intensity as a function of the crystal thickness, the extinction distance and two parameters which characterize crystal perfection over short and long ranges compared with the extinction distance.
Energy
Energy is often defined as the ability to do work. There are many forms of energy. A few examples include; Gravitational energy, Kinetic energy (energy of motion), Thermal energy (heat energy), Potential energy. Potential energy is the energy something has based on its position in the universe. A stretched elastic band has potential energy. A rock held up in the air has potential energy based on its position.