Constitutive Equations for Magnetic Active Liquids

This article is focused on the derivation of constitutive equations for magnetic liquids. The results can be used for both ferromagnetic and magnetorheological fluids after the introduced simplifications. The formulation of constitutive equations is based on two approaches. The intuitive approach is based on experimental experience of non-Newtonian fluids, which exhibit a generally non-linear dependence of mechanical stress on shear rate; this is consistent with experimental experience with magnetic liquids. In these general equations, it is necessary to determine the viscosity of a liquid as a function of magnetic induction; however, these equations only apply to the symmetric stress tensor and can only be used for an incompressible fluid. As a result of this limitation, in the next part of the work, this approach is extended by the asymmetry of the stress tensor, depending on the angular velocity tensor. All constitutive equations are formulated in Cartesian coordinates in 3D space. The second approach to determining constitutive equations is more general: it takes the basis of non-equilibrium thermodynamics and is based on the physical approach, using the definition of density of the entropy production. The production of entropy is expressed by irreversible thermodynamic flows, which are caused by the effect of generalized thermodynamic forces after disturbance of the thermodynamic equilibrium. The dependence between fluxes and forces determines the constitutive equations between stress tensors, depending on the strain rate tensor and the magnetization vector, which depends on the intensity of the magnetic field. Their interdependencies are described in this article on the basis of the Curie principle and on the Onsager conditions of symmetry.

The Jahn–Teller and Pseudo-Jahn–Teller Effects: A Unique and Only Source of Spontaneous Symmetry Breaking in Atomic Matter

In a mostly review paper, we show that the important problem of symmetry, broken symmetry, and spontaneous broken symmetry of polyatomic systems is directly related to the Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) effects, including the hidden-JT and hidden-PJT effects, and these JT effects (JTEs) are the only source of spontaneous symmetry breaking in matter. They are directly related to the violation of the adiabatic approximation by the vibronic and other nonadiabatic couplings (jointly termed nonadiabaticity) in the interaction between the electrons and nuclei, which becomes significant in the presence of two or more degenerate or pseudodegenerate electronic states. In a generalization of this understanding of symmetry, we suggest an improved (quantum) definition of stereo-chemical polyatomic space configuration, in which, starting with their high-symmetry configuration, we separate all atomic systems into three distinguishable groups: (1) weak nonadiabaticity, stable high-symmetry configurations; (2) moderate-to-strong nonadiabaticity, unstable high-symmetry configurations, JTEs, spontaneous symmetry breaking (SSB); (3) very strong nonadiabaticity, stable distorted configurations. The JTEs, inherent to the second group of systems, produce a rich variety of novel properties, based on their multiminimum adiabatic potential energy surface (APES), leading to a short lifetime in the distorted configuration. We show the role of the Curie principle in the possibilities to observe the SSB in atomic matter, and mention briefly the revealed recently gamma of novel properties of matter in its interaction with external perturbation that occur due to the SSB, including ferroelectricity and orientational polarization, leading to enhanced permittivity and flexoelectricity.

EVOLUÇÃO MORFOLÓGICA E TEXTURAL DE DIAMANTES BASEADA NO MÉTODO DA FOTOGONIOMETRIA.

The curvilinear surfaces of 47 diamonds from Macaúbas river basin (MG) were studied on theparabolic goniometer. For the diamond description primary genetic value is given to the form of thecrystal, but the secondary is given to the sculpture of the surface. Crystallographic terms: octahedroid,dodecahedroid, cuboid are usually used for classification of the form of the diamonds. For practicalpurposes this is possible to consider reasonable. To determine the figure of the curve-faced crystal,the main indicator is the position of maximum of intensity of reflected light on the stereographicprojections of crystal, but not angular sizes of the reflex. Curvilinear faces of diamonds suggest theirdissolution processes. The symmetry of crystal shape Oh for such diamonds usually decreases to C2h,C3h or C4h, which explains a crystal rotation at the dissolution according to the P. Curie principle. Thecurvilinear surfaces of the diamond crystals are possible to describe by means of fragments of thesurfaces of triaxial ellipsoid duplicated with symmetry group Oh up to twelve. Ellipsoid have semiaxisA1, A2, A3, numbered in the order of their growth, and well-ordered relatively to the crystalstructure. Axis A2 is always directed along the axis L4, but two other axes are inclined to axis L2 underthe small angle (up to 7 degrees). Angle á defines an appearance of so called “face-seam” on thesurfaces of the diamond. There are 24 curvilinear surfaces formed the dodecahedroid with “faceseams”,as a limiting shape of the diamond dissolution. Ellipsoidal surface of the diamond is thedynamic indicator of stability of the crystal structure of a homoeopolar crystal to the processes ofdissolution and partly detrition. The existence of both a triangular etching pits with the flat bottomon the surfaces (111) and a negative relief of the surface for all directions <110> shows a regenerationprocess of a diamond.

Introduction

The physical and chemical properties of crystals and textured materials often depend on direction. An understanding of anisotropy requires a mathematical description together with atomistic arguments to quantify the property coefficients in various directions. Tensors and matrices are the mathematics of choice and the atomistic arguments are partly based on symmetry and partly on the basic physics and chemistry of materials. These are subjects of this book: tensors, matrices, symmetry, and structure–property relationships. We begin with transformations and tensors and then apply the ideas to the various symmetry elements found in crystals and textured polycrystalline materials. This brings in the 32 crystal classes and the 7 Curie groups. After working out the tensor and matrix operations used to describe symmetry elements, we then apply Neumann’s Law and the Curie Principle of Symmetry Superposition to various classes of physical properties. The first group of properties is the standard topics of classical crystal physics: pyroelectricity, permittivity, piezoelectricity, elasticity, specific heat, and thermal expansion. These are the linear relationships between mechanical, electrical, and thermal variables as laid out in the Heckmann Diagram. These standard properties are all polar tensors ranging in rank from zero to four. Axial tensor properties appear when magnetic phenomena are introduced. Magnetic susceptibility, the relationship between magnetization and magnetic field, is a polar second rank tensor, but the linear relationships between magnetization and thermal, electrical, and mechanical variables are all axial tensors. As shown in Fig. 1.2, magnetization can be added to the Heckmann Diagram converting it into a tetrahedron of linear relationships. Pyromagnetism, magnetoelectricity, and piezomagnetism are the linear relationships between magnetization and temperature change, electric field, and mechanical stress. Examples of tensors of rank zero through four are given in Table 1.1. In this book we will also treat many of the nonlinear relationships such as magnetostriction, electrostriction, and higher order elastic constants. The third group of properties is transport properties that relate flow to a gradient. Three common types of transport properties relate to the movement of charge, heat, and matter. Electrical conductivity, thermal conductivity, and diffusion are all polar second rank tensor properties.