Crystal from electrostatics

In the past, ionic radii have often been compared with observed interatomic distances without much regard to the nature of the crystal from which they were derived. Recently several investigators19 have concluded that in many crystals the bond between atoms does not consist of the electrostatic attraction of only slightly deformed ions. Goldschmidt in particular has divided crystals into two classes, ionic and atomic crystals, and has shown that ionic radii (using Wasastjema s set) do not account for the observed inter-atomic distances in atomic crystals. In the following pages our crystal radii will be compared with the experimental dis-... 

D reconstruction can be performed by restoring the 3D Fourier space of the object from a series of 2D Fourier transforms of the projections. Then the 3D object can be reconstructed by inverse Fourier transformation of the 3D Fourier space. For crystalline objects, the Fourier transforms are discrete spots, i.e. reflections. In electron microscopy, the Fourier transform of the projection of the 3D electrostatic potential distribution inside a crystal, or crystal structure factors, can be obtained from HREM images of thin crystals. So one can obtain the 3D electrostatic potential distribution (p(r) inside a crystal from a series of projections by... 

Analogical molecular structure is possessed by other simple compounds such as potassium iodide, ammonium chloride, sodium hydroxide, barium nitrate, ammonium acetate and so on. In all these compounds there is a transfer of one or several electrons from one element to the other, positive and negative ions being thus formed, that are hold together in a crystal by electrostatic attraction. A bond of this kind is no genuine chemical bond in tbe correct meaning of the term, but is just,a result of Coulomb forces of attraction between opposite charges. 

The dielectric constant of liquid water at room temperature is 80. This means that two opposite electrical charges in water attract each other with a force only 1/80 as strong as in air (or a vacuum). It is clear that the ions of a crystal of sodium chloride placed in water could dissociate away from the crystal far more easily than if the crystal were in air, since the electrostatic force bringing an ion back to the surface of the crystal from the aqueous solution is only 1/80 as strong as from air. It is accordingly not surprising that the thermal agitation of the... 

Deformation density maps of crystal structures were described in Chapter 9 (see Figures 9.16 and 9.17). Methods for refining data to obtain charge information was also described. From the experimental charge parameters so derived it is possible to map the electrostatic potential in the crystal,or for a molecule or group of atoms removed from the crystal. These electrostatic potential maps show which areas around a molecule are electronegative and which are electropositive. 

Regardless of the type of chemical bond that forms, the net force between two chemically bound atoms results from electrostatic attraction [16], The attractive component, / iiii, of the total bond energy between two atoms is a function of the distance between them, r. The normal form of the attractive force, based on Coulomb s law, for ionic crystals is... 

Cross-linked crystals from subtilisin exhibited 27 times less activity than soluble subtilisin in the hydrolysis of benzoyl-L-phenylalanine ethyl ester. Denaturation of the enzyme and restrictions from substrate-dependent internal diffusion were ruled out. A shift in the pH-dependence of the maximum activity to higher pH-values was observed which was explained by inter molecular electrostatic... 

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