Calcium titanate-CaTiO3 (perovskite) has been used in various industrial applications due to its dopant/doping mechanisms. Manipulation of defective grain boundaries in the structure of perovskite is essential to maximize mechanical properties and stability; therefore, the structure of perovskite has attracted attention, because without fully understanding the perovskite structure and diffracted planes, dopant/doping mechanisms cannot be understood. In this study, the areas and locations of atoms and diffracted planes were designed and investigated. In this research, the relationship between Young’s modulus and planar density of unit cell, super cells (2 × 2 × 2) and symmetry cells of nano CaTiO3 is investigated. Elastic constant, elastic compliance and Young’s modulus value were recorded with the ultrasonic pulse-echo technique. The results were C11 = 330.89 GPa, C12 = 93.03 GPa, C44 = 94.91 GPa and E = 153.87 GPa respectively. Young’s modulus values of CaTiO3 extracted by planar density were calculated 162.62 GPa, 151.71 GPa and 152.21 GPa for unit cell, super cells (2 × 2 × 2) and symmetry cells, respectively. Young’s modulus value extracted by planar density of symmetry cells was in good agreement with Young’s modulus value measured via ultrasonic pulse-echo.
In this chapter, we are going to study the following:(i)The elements of group theory.(ii)Types of groups, order of the group, classes, and other related aspects.(iii)Construction of group multiplication tables for all crystallographic point groups using both International and Schoenflies notations for the first time in crystallographic history.
This book discusses symmetry representations of molecular vibrations, their matrix representation, and group theory.
of symmetry , point groups, , , In this chapter, we are going to discuss the following: (i)To develop the concept of molecular vibrations in diatomic and polyatomic molecules. (ii)To develop the relationship between reducible and irreducible representations of symmetry operations. (iii)To determine the character of matrices of some fundamental symmetry operations. (iv)The derivation of normal modes of vibration for some selected nonlinear and linear and molecules.
This chapter describes the following fundamental topics whose knowledge will form the basis to understand the contents of the subsequent chapters. They are: (i)Fundamental aspects of molecular and crystal symmetries. (ii)Types and properties of matrices. (iii)Matrix representation of symmetry operations. (iv)Molecular and crystallographic point groups. (v)A new method to understand the distribution of symmetry operations among the crystallographic point groups from the least symmetric system to the most symmetric system. (vi)Two important point group notations, Schoenflies and International.
the symmetry / In this chapter, we are going to discuss the following important aspects: (i)The concepts of reducible and irreducible representations. (ii)Basic features of orthogonality theorem. (iii)Constructions of character tables of non-abelian groups of finite order. (iv)Constructions of character tables of abelian and cyclic groups of finite/infinite order.
The role of the rotational coherence in the air lasing at 391 nm, corresponding to the coherent \(\mathrm{B}{}^2\Sigma _\mathrm{u}^+(v' = 0)-\mathrm{X}{}^2\Sigma _\mathrm{g}^+(v'' = 0)\) emission of N\(_2^+\) exposed suddenly to an ultrashort intense near-IR laser field, is investigated theoretically by referring to the recent experimental and theoretical studies on the air lasing that elucidated the mechanism of the population inversion between the \(\mathrm{B}{}^2\Sigma _\mathrm{u}^+\) and \(\mathrm{X}{}^2\Sigma _\mathrm{g}^+\) states in terms of the sudden turn-on of the interaction of N\(_2^+\) with the laser field combined with the post-ionization coupling among the \(\mathrm{X}{}^2\Sigma _\mathrm{g}^+\), \(\mathrm{A}{}^2\Pi _\mathrm{u}\), and \(\mathrm{B}{}^2\Sigma _\mathrm{u}^+\) states of N\(_2^+\).
Inelastic collision processes, namely, processes of energy exchange of translational motion (T-T exchange), a transformation of translational, and rotational energy (R-T exchange), a transformation of vibrational energy (V-T, V-R and V-V exchange) are discussed briefly. Then perturbation-facilitated and perturbation-irrelevant collision-induced non-adiabatic transitions (CINATs), and other processes in which CINATs occur, are considered. CINATs between halogen ion-pair states are examined in detail.
In this chapter, the concept of photomagnetic effect in copper(II)-octacyanidometallate(IV) systems and its various aspects have been introduced. Multifunctional cyanido-bridged metal assemblies attract much attention due to their great importance for fundamental research as well as their potential application in various technologies. Among the numerous advantages of this type of assemblies, the vast structural diversity should be distinguished, as it allows for various electronic states by a combination of metal ions and ligand, resulted in their functionalities. The most excellent examples of such materials are photomagnetic compounds revealing switching between different magnetic states by stimulation with electromagnetic radiation. Herein, various CuII-[MIV(CN)8]4− complexes with unique characters of photoinduced magnetization, milestones in understanding the mechanism of photomagnetic behavior and the impact of various factors on their photomagnetic phenomena are presented.
We numerically study the dynamics of the formation of optical vortex from collimated Gaussian beam behind a spiral phase plate, and assess the characteristic scale of azimuthal instability developing in a Kerr medium. The near zero values of intensity on axes arise shortly after the plate but the ring profile is formed at the distance of approximately half of the diffraction length. The break-up of the vortex into several hot spots in the Kerr medium is more rapid for the large-scale noise. The transformation of the vortex spatial spectrum is analyzed along with changes in its phase profile. The interference of the self-focusing mode and the radiation extending to the periphery leads to the formation of rings in the beam spectrum.
The chapter deals with elementary processes, i.e., the simple processes which proceed in one stage. The definitions of differential and total cross-sections, microscopic rate constants, and probabilities of elementary processes are introduced. The detailed balance principle, adiabatic approximations, as well as potential energy curves and surfaces, are discussed. Different types of intermolecular interactions, descriptions of collisional processes and reactions including nonadiabatic transition using potential energy curves and surfaces are examined.
In the real world water and ice always have boundaries, being confined by the solid or liquid materials, representing the sample in contact with a gas, vacuum, another liquid, or serving as a solvent of electrolyte solution. Interestingly, the properties of such “finite” water, ice, or aqueous media, can differ from those for the theoretical boundless water. In this chapter, we discuss the electrical properties of aqueous electrolytes, the electrodynamics of confined water, the effect of a strong electric field on water viscosity, and the electrification of water droplets, and other systems where the role of boundaries on the properties of water is important, in an external electric field. The questions regarding the role of water in atmospheric phenomena, and the future of the aqueous electrochemical energy systems (fuel cells, supercapacitors, flow batteries, electrolyzers) are discussed.
