Effective crystal volume

Finite resolution and partial volume effects. Although this can occur in other areas of imaging such as MRS, it is particularly an issue for SPECT and PET because of the finite resolution of the imaging instruments. Resolution is typically imaged as the response of the detector crystal and associated electron to the point or line source. These peak in the center and fall off from a point source, for example, in shapes that simulate Gaussian curves. These are measures of the ability to resolve two points, e.g. two structures in a brain. Because brain structures, in particular, are often smaller than the FWHM for PET or SPECT, the radioactivity measured in these areas is underestimated both by its small size (known as the partial volume effect), but also spillover from adjacent radioactivity... 

The crystallizer was an agitated vessel with an Inside diameter of 9.0 cm and a volume of about 1 1. It was equlppet with four vertical baffles, a water jacket to keep the solution temperature constant, and a nozzle through which nitrogen gas was Introduced In several experiments to suspend a speed crystal more effectively In the solution. Agitation was accomplished with a 5.0 cm stainless steel marine propeller having three blades driven by a variable speed motor. 

Effect of illuminating a larger crystal volume and focusing the beam on the detector... 

The spontaneous magnetostriction has been measured by single crystal x-ray diffraction between 10 and 300 K (Kusz et al. 2000). As can be seen from figs 38 and 39, both compounds show pronounced linear as well as volume effects. Gd3Ni is characterized by a large positive spontaneous magnetostriction in a-direction (the estimated value at 0 K is (Aa/a)mag 2.9 x 10 3), whereas the effects in b- and c-direction are about two... 

Polyethylene crystals change shape with time at temperatures between the crystallisation temperature and the final melting point [42]. The process is commonly referred to as crystal thickening because the major effect is that the crystals increase their dimensions along the c axis. These changes may occur without any change in crystal volume, i.e. crystal thickening is associated with a lateral contraction of the crystals (Fig. 9). A second option is that... 

In this equation, h is Planck s constant divided by 2tt, V is the crystal volume, T is temperature, fej, is Boltzmann s constant, phonon frequency, is the wave packet, or phonon group velocity, t is the effective relaxation time, n is the Bose-Einstein distribution function, and q and s are the phonon wave vector and polarization index, respectively. 

Up the 50% of the total crystal volume represents pore space, and high effective concentrations of organic - substrate couples can thus be generated. 

The silver nitrate is purified by repeated crystallization from acidified solutions, followed by fusion. The purity of the salt is proved by the absence of the so-called volume effect, the weight of silver deposited by a given quantity of electricity being independent of the volume of liquid in the coulometer this means that no extraneous impurities are included in the deposit. The solution of silver nitrate employed for the actual measurements should contain between 10 and 20 g. of the salt in 100 cc. it should be neutral or slightly acid to methyl red indicator, after removal of the silver by neutral potassium chloride, both at the beginning and end of the electrolysis. The anode should be of pure silver with an area as large as the apparatus permits the current density at the anode should not exceed 0.2 amp. per sq. cm. To prevent the anode slime... 

As an application of this kind of calculation, we refer to the case of liquid crystals. Okan< et al. have discussed the role of excluded volume effect on the molecular orientation in th< interface involving liquid crystals. They used spherocylinder systems, but considered only limited Ccise of orientation. 

The application of the plane wave basis set implies that the periodicity is taken into account and the method is therefore well suited for the simulation of the crystal field effects. For a recent review of Car-Parrinello methodology see Ref. [31]. With Car-Parrinello method the proton motion in PANO including the effects of crystal environment was simulated. The molecular dynamics simulation was carried out at a constant volume, i.e. the unit cell parameters were fixed during the simulation. Fictitious orbital mass was set to 150 a.u. (note that 1 a.u. corresponds to the electron mass) and the propagation time step was set to 2 a.u. 

An interesting situation arises in an ordered matrix such as liquid crystals [131]. When a molecule is transformed from a linear shape (e.g., trans form) to a bended structure (e.g., cis form), it changes the environment dramatically and increases the void volume around the solute. This volume expansion will induce a strong TG signal. One of the causes of the large optical nonlinearity of liquid crystals is attributed to this volume effect. 

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