Lattice complex notation

Laves (1930,1956) recognising the difficulty in using a lattice-complex notation for the description of structure types made the distinction between four different homogeneous Bauverbande I (island), C (chain), N (net), L (lattice). Corresponding small letters are used for heterogeneous ones. Coordination numbers and distances are added. 

Hellner (1965) has proposed a nomenclature for inorganic structure types based on the lattice complex notation, which is useful for compounds with higher symmetry, but which becomes very complicated for compounds of lower symmetry. Examples are Fd-3m, F" 222+D,T for Al2Mg04 (spinel), and Pmcn, (h)n C22+00i/2l2xyA2ni/4 1/4F for (Mg,Fe)2Si04 (olivine). 

It must be realized that actually for each oxygen ion built into the lattice, according to (i) a vacant lattice site must be created in the sublattice of nickel ions. This is due to the geometrical impossibility of accommodating excess oxygen in the lattice. Excess oxygen really means nickel deficiency. More complex notations than the notation used here are necessary to deal with this situation (51) but for our purpose we need not go into this. If now the ionization equilibrium... 

There is a difference between the ciystai chemicai formula of a structure and the symbol of a structure type. The crystal chemical formula of a structure (or structural formula of a compound) corresponds to the chemical formula of the compound with the addition of superscripts, subscripts, parentheses, etc., expressing its various structural characteristics. The symbol of a structure type represents a certain kind of structural arrangement and may be based on various notations such as alphabetic letters, lattice complexes or crystal chemical formulae. 

I have to say a word about the notation. It is the same as that used in other books about this subject. This notation might sometimes look complicated. The basic concepts (linear oscillator. Hook s law, etc.) are simple but the lattice with a basis introduces an unavoidable complex notation. Experience has shown, however, that students become accustomed to the notation very quickly. Therefore, there is no reason to be discouraged by this. Whenever possible I have tried to use a simpler or condensed notation. Appendix Q contains the most important physical constants and units used in this book. 

Gallium (10 % of the earth s crust) is present in zinc blende, which may contain up to 0.5%, and in certain e.g. British) coal ash. The metal, which is deposited by electrolysis from alkaline solutions of its salts, is silvery-white, hard and brittle. The orthorhombic crystal has a complex lattice. The co-ordination is strictly one-fold, a given gallium atom having one atom situated at 2.43 A and six others at distances varying from 2.70 to 2.79 A. This co-ordination is denoted by 1 + 6 the notation applies only if the six atoms are separated from the reference atom by a distance not greater than 1.2 times that of the nearest one. The metal is stable in dry air and does not decompose water. It dissolves in caustic alkalis and in mineral acids, other than nitric which renders it passive. Its chemistry (Fig. 151) is, in fact, very similar to that of aluminium. 

Dependence of Adsorption Parameter K on Salt Concentration The physical meaning of Equation 5.48 can be revealed by chemical-reaction considerations. For simplicity, let us consider Langmuir-type adsorption i.e., we treat the interface as a two-dimensional lattice. We will use the notation Bg for the fraction of the free sites in the lattice, 0, for the fraction of sites containing adsorbed surfactant ion S , and 02 for the fraction of sites containing the complex of an adsorbed surfactant ion + a bound counterion. Obviously, we can write 0q -1- 0i -1- 02 = F The adsorptions of surfactant ions and counterions can be expressed in the form ... 

Note the ground-state atomic term symbol for Cr is F, which splits into T2, Ti and A2 for an octahedral transition metal complex. For more information regarding term symbol notation and absorption spectra for transition metal complexes, see Shiiver et al. Inorganic Chemistry, 4th ed., W. H. Freeman New York, 2006. http //www.scribd.com/doc/6672586/Electronic-Spectroscopy-l Note excited electrons give off their energy via infrared emission and thermal interactions with the corundum crystal lattice, referred to as electron-phonon (lattice vibrations) interactions. 

We turn our attention next to specific examples of real crystal surfaces. An ideal crystal surface is characterized by two lattice vectors on the surface plane. Hi = aix + aiyS, and H2 = 02xX -I- a2yy. These vectors are multiples of lattice vectors of the three-dimensional crystal. The corresponding reciprocal space is also two dimensional, with vectors bi, b2 such that b aj = IrrStj. Surfaces are identified by the bulk plane to which they correspond. The standard notation for this is the Miller indices of the conventional lattice. For example, the (001) surface of a simple cubic crystal corresponds to a plane perpendicular to the z axis of the cube. Since FCC and BCC crystals are part of the cubic system, surfaces of these lattices are denoted with respect to the conventional cubic cell, rather than the primitive unit cell which has shorter vectors but not along cubic directions (see chapter 3). Surfaces of lattices with more complex structure (such as the diamond or zincblende lattices which are FCC lattices with a two-atom basis), are also described by the Miller indices of the cubic lattice. For example, the (001) surface of the diamond lattice corresponds to a plane perpendicular to the z axis of the cube, which is a multiple of the PUC. The cube actually contains four PUCs of the diamond lattice and eight atoms. Similarly, the (111) surface of the diamond lattice corresponds to a plane perpendicular to the x -I- y -I- z direction, that is, one of the main diagonals of the cube. 

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