Primary Valence Lattices

If we are to understand the structure of a crystal lattice fully and are interested both in the mutual position of the atoms and the magnitude and nature of the forces, we must take into account the interval rule and the other properties of the substance in addition to the above described geometrical considerations and try to merge them into a uniform design. 

The same is true for the majority of molecular lattices already discussed. 

The whole crystal is held together in all directions by identical forces and demarcation of a definite closed region is impossible geometrically and dynamically. Such lattices are familiar among the metals, e.g. Na, Mg, Cu, W, etc. in which cohesion is provided for by metallic bonding 

In conclusion, it may be remarked that many natural proteins and resins—the keratin of nails, hair and feathers, colophony and others— form primary valence lattices which may possess such great regularity that they give at times very definite x-ray interferences, as shown by interesting experiments of Astbury.  

The properties of the primary valence lattice enumerated above— in fusibility, insolubility, strength and density—make it difficult to 

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We are just as well informed regarding the structure of calcium silicide, which was described by Bohm and Hassel as a primary valence lattice of six-membered silicon rings linked together by calcium bridges. Fig. 46 shows diagrammatically the arrangement of atoms in this lattice as elucidated by thorough x-ray structure analysis. 

A specially good example showing how a large group of important compounds can develop all the above described types—primary valence lattices, primary valence networks and primary valence chains—is afforded by the silicates whose structure elucidation is due in the first place to the experiments of W. L. Bragg and his co-workers over many years. For these very compounds the old method borrowed from organic chemistry of description by the aid of constitutional formulas was shown to be inappropriate. 

This comprises all lattices which cohere by homopolar primary valences in all three directions in space. The character of the linkage has already... 

In graphite, the distances between adjacent atoms in the principal plane are 1.45 A, while perpendicular thereto the smallest distance amounts to 3.3 A. We have before us a lattice which coheres in two directions by normal primary valences and by secondary valences in the third direction... 

Proceeding from graphite, let us finally imagine a carbon lattice, which coheres in one direction through primary valences and in the two other directions by secondary valences. Such a structure is impossible from carbon atoms alone where tetrahedral valence holds, but we can conceive of its being realized, e.g. from a carbon chain of double bonds alone. Its density must lie, according to the distance law, between 0.8 and 1.1, according to the particular manner of separation between the chains. 

Substances in which lattice structure is provided for in all three directions by homopolar primary valences, while the cohesion of the lattice cells is due to the metallic bond, may be present in many intermetallic compounds although nothing definite can be said here regarding the exact type of linkage involved. 

These include, notably, the layer lattices which cohere in two directions by primary valences and in the third by secondary valences examples, which we shall later discuss in greater detail, are Cdl2, M0S2, Asis, talc, graphitic acid and siloxene. The anisotropy of the linkage type is very markedly expressed in them by the laminar habit and by the mechanical properties. To this type belong also reticulate filamentous lattices such as exist in vulcanized rubber and in numerous synthetic high polymers. 

We come next to a type which is of very special importance to natural and synthetic organic high polymers to the filament lattices which cohere in one direction by primary valences and in the other two by van der Waals forces. The chief representatives of this class, which will be discussed in great detail in the second volume of this work, are cellulose, chitin, rubber, proteins and a large number of synthetic high polymers such as polystyrene, polyvinyl acetate, polyacrylic esters, polyethylene oxide, etc. 

The next step leads us to those compounds, discussed above, in which the lattice itself is formed in all three directions by secondary valence forces, but in which the lattice units are kept together by primary valences. We have here the large number of molecular lattices consisting of compact units, such as CI2, CH4, CeHe and we arrive finally at the inert gases in whose lattice-like structure only secondary valence forces participate. 

If experience gained from layer lattices is. applied to the chain lattices, which are also frequently named fiber lattices, it is to be expected that the cohesion of the primary valence chains will stamp the whole structure and that permutoid reaction will be present to a still higher degree than in layer lattices, because here the strong cohesion due to primary valence acts only in a single direction. We may further assume that the diffraction effects of such primary valence chains will exhibit certain similarities to diffraction phenomena in linear lattices. 

Natural high polymeric compounds, like high molecular weight mixtures, show only reflections corresponding to the intra-molecular periodicity, so that here also primary valence chain lattices are involved. 

The main forces, which prevail in these lattices are those between the silicon and oxygen atoms which are best viewed as homopolar primary valences, although they probably have in part a certain heteropolar aspect. 

The fee lattice of the coinage metals has 1 valency electron per atom (d °s ). Admixture with metals further to the right of the periodic table (e.g. Zn) increases the electron concentration in the primary alloy ( -phase) which can be described as an fee solid solution... 

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