Density displacement factor

About Dosage Replacement Factor, Density Displacement Factor and Displacement Value... 

The density displacement factor (DDF) of an active substance is the number of parts by weight of the active substance that displaces one part of hard fat [43] and is therefore equal to 1/f. 

Regularly, for the dosage replacement factor (f) other terms are used, for example replacement factor, dose-replacement factor and even displacement factor. The density displacement factor (DDF) is frequently called displacement value the terms displacement factor and density factor are used too. To recognise what authors mean, it is good to realise that mostly f < 1 and DDF = 1/f > 1. 

Sometimes the replacement value is used. This is the weight of base displaced by the active substance (per suppository). Used is also the term displacement value. The replacement value is calculated by multiplying the weight of active substance per suppository by the dosage replacement factor or by dividing the weight of active substance per suppository by the density displacement factor [44]. 

Equation (Bl.8.6) assumes that all unit cells really are identical and that the atoms are fixed hi their equilibrium positions. In real crystals at finite temperatures, however, atoms oscillate about their mean positions and also may be displaced from their average positions because of, for example, chemical inlioniogeneity. The effect of this is, to a first approximation, to modify the atomic scattering factor by a convolution of p(r) with a trivariate Gaussian density function, resulting in the multiplication ofy ([Pg.1366]

Iditional importance is that the vibrational modes are dependent upon the reciprocal e vector k. As with calculations of the electronic structure of periodic lattices these cal-ions are usually performed by selecting a suitable set of points from within the Brillouin. For periodic solids it is necessary to take this periodicity into account the effect on the id-derivative matrix is that each element x] needs to be multiplied by the phase factor k-r y). A phonon dispersion curve indicates how the phonon frequencies vary over tlie luin zone, an example being shown in Figure 5.37. The phonon density of states is ariation in the number of frequencies as a function of frequency. A purely transverse ition is one where the displacement of the atoms is perpendicular to the direction of on of the wave in a pmely longitudinal vibration tlie atomic displacements are in the ition of the wave motion. Such motions can be observed in simple systems (e.g. those contain just one or two atoms per unit cell) but for general three-dimensional lattices of the vibrations are a mixture of transverse and longitudinal motions, the exceptions... 

For XH bonds, where X is any heavy atom, the hydrogen electron density is not thought to be centered at the position of the hydrogen nucleus but displaced along the bond somewhat, towards X. The MMh- force field reduces the XH bond length by a factor of 0.915 strictly for the purposes of calculating van der Waals interactions with hydrogen atoms. 

The discussion so far relates to the motion of a single spherical particle in an effectively infinite expanse of fluid. If other particles are present in the neighbourhood of the sphere, the sedimentation velocity will be decreased, and the effect will become progressively more marked as the concentration is increased. There are three contributory factors. First, as the particles settle, they will displace an equal volume of fluid, and this gives rise to an upward flow of liquid. Secondly, the buoyancy force is influenced because the suspension has a higher density than the fluid. Finally, the flow pattern of the liquid relative to... 

For vanadium, the ratios are smaller, and the dynamic density maps do not show a distinct maximum in the cube direction. The difference is attributed to anharmonicity of the thermal motion. Thermal displacement amplitudes are larger in V than in Cr, as indicated by the values of the isotropic temperature factors, which are 0.007 58 and 0.00407 A2 respectively. As in silicon, the anharmonic displacements are larger in the directions away from the nearest neighbors, and therefore tend to cancel the asphericity of the electron density due to bonding effects. 

A significant fraction, more than 25%, of the low-density polyethylene (LDPE) (Sec. 3-14a) produced by radical polymerization consists of various copolymers of ethylene. LDPE has come under increasing economic pressure in recent years because of a combination of factors [Doak, 1986]. High-density polyethylene (HDPE) has displaced LDPE in applications such as blow-molded bottles and thin films where the increased strength of HDPE is preferred over the clarity of LDPE. Linear low-density polyethylene (LLDPE) (Sec. 8-1 lc) competes effectively with LDPE in terms of both cost and properties. New producers of ethylene have entered the LDPE market because of a lack of alternatives for their feedstocks. Many LDPE producers use copolymerization as a strategy to obtain products more resistant to displacement by HDPE and LLDPE. 

T(S) is the Debye-WaUer factor introduced in (2). The atomic form factors are typically calculated from the spherically averaged electrcai density of an atom in isolation [24], and therefore they do not contain any information on the polarization induced by the chemical bonding or by the interaction with electric field generated by other atoms or molecules in the crystal. This approximation is usually employed for routine crystal stmcture solutions and refinements, where the only variables of a least square refinement are the positions of the atoms and the parameters describing the atomic displacements. For more accurate studies, intended to determine with precisicai the electron density distribution, this procedure is not sufficient and the atomic form factors must be modeled more accurately, including angular and radial flexibihty (Sect. 4.2). 

An examination of the stereochemistry of the H+ ion is complicated by a number of factors. Because it has no electron core, hydrogen is difficult to locate using X-rays which are scattered by electrons. In earlier structure determinations its presence was often ignored because it made no contribution to the X-ray diffraction pattern and could not therefore be located. Even when H is included in the model, its position can rarely be accurately determined and in any case the centre of its electron density is usually displaced from the nucleus towards the donor anion by around 20 pm. Accurate positions of the H+ nuclei can be found using neutron diffraction which has provided sufficient information to reveal the essential characteristics of hydrogen bond geometries, but in many of the structures determined by X-ray diffraction the positions of the H cations have had to be inferred from the positions of their neighbouring anions. 

A particular conclusion from this theoretical analysis is that, if a crack has faces that are separated by a thin layer of fluid, so that normal components of traction and displacement are transmitted across the crack but the faces are free with regard to shear components of traction and displacement, then there will be a scattered wave however thin the fluid layer is. This is perhaps not surprising. A Rayleigh wave can exist only because solids can support both longitudinal and shear waves, and the greater part of the displacement in a Rayleigh wave is shear in character ( 6.3). Of course, liquids can support shear stress over a short distance. In a liquid of viscosity r/, and density po, at a frequency o) the amplitude of a shear wave decays by a factor e over a distance... 

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