The plane net

To summarize, the categories of point defects possible for these two types of lattices are illustrated are  

Schottky defects (absence of both cation and anion) 

SIS Frenkel defects (Cation vacancy plus the same cation as interstitial) 

All of these point defects are intrinsic to the solid. The factors responsible for their formation are entropy effects (point defect faults) and impurity effects. At the present time, the highest-purity materials available still contain about 1.0 part per billion of various impurities, yet are 99.9999999 % pure. Such a solid will contain about 10 impurity atoms per mole. So it is safe to say that all solids contain impurity atoms, and that it is unlikely that we shall ever be able to obtain a solid which is completely pure and does not contain defects. 

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These, then, cire the set of possible defects for the Plane Net, and the following summarizes the types of intrinsic defects expected. Note that we have used the labelling V = vacancy i = interstitial M = cation site X = anion site and s = surface site. We have already stated that surface sites are special. Hence, they are included in our listing of intrinsic defects. 

Whether you recdize it or not, we have already developed our own symbolism for defects and defect reactions based on the Plane Net. It might be well to compeu e our system to those of other authors, who have also considered the same problem in the past. It was Rees (1930) who wrote the first monograph on defects in solids. Rees used a box to represent the cation vacancy, as did Libowitz (1974). This has certain advantages since we can write equation 3.3.5. as shown in the following ... 

Now, let us consider how such defects arise in any given solid. The easiest way to visualize how intrinsic defects occur in the solid is to study the PLANE NET. Imagine that we have M as eations and X as anions (we shall... 

For the plane net, we can expect the following types of intrinsic defects ... 

In Eq. (23.39), uq is the far-held velocity, so velocities at position A in front of the plane net were selected for calculation. Velocities at position G were selected for validation of the calculation model proposed. The model setting and measurement points during experiments are shown in Fig. 23.16. 

As shown in Table 23.3, an average velocity reduction of 12.4% was observed behind the plane net. Results calculated according to Eq. (23.39) agree well with the experimental data. The calculated results are also consistent with experimental results presented by Fredriksson, in which an approximate 10% reduction in velocity was found for a sea-station cage. 

M. Tauti, The force acting on the plane net in motion through the water, Bttll. Jpn. Soc. Scientific Fisheries 3(1), 1-4 (1934). 

We have now dealt with the plane nets and the polyhedra. The condition for a 3D-net is consequently ... 

This subject has a long history and important early papers include those by Deijaguin and Landau [29] (see Ref. 30) and Langmuir [31]. As noted by Langmuir in 1938, the total force acting on the planes can be regarded as the sum of a contribution from osmotic pressure, since the ion concentrations differ from those in the bulk, and a force due to the electric field. The total force must be constant across the gap and since the field, d /jdx is zero at the midpoint, the total force is given the net osmotic pressure at this point. If the solution is dilute, then... 

Mixtures containing equal quantities of enantiomers are called racemic mixtures Racemic mixtures are optically inactive Conversely when one enantiomer is present m excess a net rotation of the plane of polarization is observed At the limit where all the molecules are of the same handedness we say the substance is optically pure Optical purity or percent enantiomeric excess is defined as... 

The complex CUCN.NH3 provides an unusual example of CN aeting as a bridging ligand at C, a mode which is common in p,-CO complexes (p. 928) indeed, the complex is unique in featuring tridentate CN groups which link the metal atoms into plane nets via the Cu... 

In accordance with Ohm s law, if we were to double the intensity X of the electric field, the current would be doubled that is to say, the plane CD would have to be placed at twice the distance from AB. If the number of conduction electrons per unit volume is p, and the distance between the planes CD and AB is denoted by v, we have n = pv, since we are discussing the unit area. Hence the net resultant charge transported in unit time across AB, that is, the current density, is given by... 

Considering the diffusion, in the T-direction, of one constituent A of a mixture across the plane a-a, if the numerical concentration is on one side of the plane and on the other side at a distance of jk, the net rate of passage of molecules per unit area... 

A considerable body of scientific work has been accomplished in the past to define and characterize point defects. One major reason is that sometimes, the energy of a point defect can be calculated. In others, the charge-compensation within the solid becomes apparent. In many cases, if one deliberately adds an Impurity to a compound to modify its physical properties, the charge-compensation, intrinsic to the defect formed, can be predicted. We are now ready to describe these defects in terms of their energy and to present equations describing their equilibria. One way to do this is to use a "Plane-Net". This is simply a two-dimensional representation which uses symbols to replace the spherical images that we used above to represent the atoms (ions) in the structure. 

It is also easy to see that we can stack a series of these "NETS" to form a three-dimensional solid. We can also suppose that the same type of defects wiU arise in our Plane Net as in either the homogeneous or heterogeneous soM and so proceed to label such defects as Mi, meaning an interstitial In the same way, we label a cation vacancy as Vm,... 

Returning to the subject of lattice defect formation, we can now proceed to write a series of defect reactions for the defects which we found for our plane net ... 

Draw one or more "plane-nets" for the "P" eation eombined with a "U" anion. Indicate all of the possible defects that can appear. Write the symbol of each as you proceed. Include pairs of defects as needed. 

Write equations for as many of the thirty (30) defects reactions of your "PU" plane-net as you can. Do not forget the defect-pairs. 

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