Deformation density definition

Clearly the form of a deformation density depends crucially on the definition of the reference state used in its calculation. A deformation density is therefore meaningful only in terms of its reference state, which must be taken into account in its interpretation. As we will see shortly, the theory of AIM provides information on bonding directly from the total molecular electron density, thereby avoiding a reference density and its associated problems. But first we discuss experimentally obtained electron densities. 

As noted above, in the traceless definition the /th-order multipoles are the sole contributors to the /th electrostatic moments. This implies that the traceless moments derived from the total density p(r) and from the deformation density Ap(r) are identical, that is, ,mp(p) = 0,mp(Ap) for / > 2. 

Figure 9 shows the deformation densities in crystals of Mo2(CH3C02)4. They show the remarkable feature at the center of the Mo—Mo bond with a diffuse but definite positive region with a height of 0.2 e A-3. This positive region extends perpendicularly to the... 

As noted in Chapter 2, deformation densities suffer from ambiguities in definition of reference state and are not (even in theory) directly related to other bond properties. Inspection of the total molecular density or its derivative may ultimately prove more valuable (Bader et al., 1979 Bader, 1985). A start has been made in this endeavor by Swope and Downs (1988), who found features in the Laplacian of the density for B-O bonds... 

The apparent bulk that hair assumes after grooming is an important aesthetic characteristic often referred to as body, which can be considered a property associated with Robbins term style retention. Tolgyesi and co-workers (67) proposed the following definition of this hair assembly property Body is a measure of a hair mass s resistance to and recovery from externally induced deformation. This definition correlates well with the descriptive components springiness, volume, and stiffness that Wedderbum and Prall have obtained by applying statistical techniques to word association (58). The structural strength and resiliency of the hair mass are influenced by a number of independent parameters. Tolgyesi has identified the five most important parameters as fiber density... 

Conventional implementations of MaxEnt method for charge density studies do not allow easy access to deformation maps a possible approach involves running a MaxEnt calculation on a set of data computed from a superposition of spherical atoms, and subtracting this map from qME [44], Recourse to a two-channel formalism, that redistributes positive- and negative-density scatterers, fitting a set of difference Fourier coefficients, has also been made [18], but there is no consensus on what the definition of entropy should be in a two-channel situation [18, 36,41] moreover, the shapes and number of positive and negative scatterers may need to differ in a way which is difficult to specify. 

Density When a powder is poured into a container, the volume that it occupies depends on a number of factors, such as particle size, particle shape, and surface properties. In normal circumstances, it will consist of solid particles and interparti-clulate air spaces (voids or pores). The particles themselves may also contain enclosed or intraparticulate pores. If the powder bed is subjected to vibration or pressure, the particles will move relative to one another to improve their packing arrangement. Ultimately, a condition is reached where further densilication is not possible without particle deformation. The density of a powder is therefore dependent on the handling conditions to which it has been subjected, and there are several definitions that can be applied either to the powder as a whole or to individual particles. 

In modem physics, there exist alternative theories for the equilibrium statistical mechanics [1, 2] based on the generalized statistical entropy [3-12]. They are compatible with the second part of the second law of thermodynamics, i.e., the maximum entropy principle [13-14], which leads to uncertainty in the definition of the statistical entropy and consequently the equilibrium probability density functions. This means that the equilibrium statistical mechanics is in a crisis. Thus, the requirements of the equilibrium thermodynamics shall have an exclusive role in selection of the right theory for the equilibrium statistical mechanics. The main difficulty in foundation of the statistical mechanics based on the generalized statistical entropy, i.e., the deformed Boltzmann-Gibbs entropy, is the problem of its connection with the equilibrium thermodynamics. The proof of the zero law of thermodynamics and the principle of additivity... 

Poisson s ratio depends on the dimensionality of the structure and cross link density. A three dimensional network structure has lower v value than that of a two dimensional structure, which, in turn, is less than that of a one-dimensional structure since the number of bonds resisting a transverse deformation decreases in that order. However, in glasses which are isotropic, the definition of dimensionality becomes less rigorous. Typical three dimensional glasses like Si02 or Ge02 have v 0.15... 

Relative density, 203 Relaxation time, 622, 638 Resin pricing, 66 Resistance to chemicals, 52 Resistance to oxidation, 52 Resistance to thermal deformation, 83 Rheological properties, 129 Rheological studies, 186 Rheology, basic definitions and equations, 618... 

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