Zinc lattice

The foregoing considerations become modified for certain systems, especially those of more than one component, such as alloys, and here a special kind of change, known as an order-disorder transition, can occur. The phenomena shown by the alloy of copper and zinc known as jS-brass will introduce us to a matter of some general importance. At low temperatures the alloy consists of a regular lattice of copper atoms, one at each corner of a series of cubes, and of a similar lattice of zinc atoms, so disposed that each cube of the copper lattice has a zinc atom at its centre and each cube of the zinc lattice a copper atom. The two interpenetrating simple cubic lattices thus give what is called a body-centred cubic lattice. 

The activator polyether, in this case dioxane, opens-up the cyanide-zinc lattice in a manner that permits coordination with oxirane, which displaces the activator polyether. This is followed by hydroxyl attack, in this case from water, and initiation of polymerization. Polymerization proceeds by rearward attack of alkoxide on oxirane, so that the polyether produced is terminated, in the case of propylene oxide, by secondary hydroxyl groups. 

Zincill) chloride. ZnCl2, is the only important halide—it is prepared by standard methods, but cannot be obtained directly by heating the hydrated salt. It has a crystal lattice in which each zinc is surrounded tetrahedrally by four chloride ions, but the low melting point and solubility in organic solvents indicate some covalent... 

Various other soft materials without the layer—lattice stmcture are used as soHd lubricants (58), eg, basic white lead or lead carbonate [598-63-0] used in thread compounds, lime [1305-78-8] as a carrier in wire drawing, talc [14807-96-6] and bentonite [1302-78-9] as fillers for grease for cable pulling, and zinc oxide [1314-13-2] in high load capacity greases. Graphite fluoride is effective as a thin-film lubricant up to 400°C and is especially useful with a suitable binder such as polyimide varnish (59). Boric acid has been shown to have promise as a self-replenishing soHd composite (60). 

One feature of oxides is drat, like all substances, they contain point defects which are most usually found on the cation lattice as interstitial ions, vacancies or ions with a higher charge than dre bulk of the cations, refened to as positive holes because their effect of oxygen partial pressure on dre electrical conductivity is dre opposite of that on free electron conductivity. The interstitial ions are usually considered to have a lower valency than the normal lattice ions, e.g. Zn+ interstitial ions in the zinc oxide ZnO structure. 

Another source of departure from stoichiometry occurs when cations are reduced, as for example in tire reduction of zinc oxide to yield an oxygen-defective oxide. The zinc atoms which are formed in tlris process dissolve in the lattice, Zn+ ions entering interstitial sites and the coiTesponding number of electrons being released from these dissolved atoms in much the same manner as was found when phosphorus was dissolved in the Group IV semiconductors. The Kroger-Viirk representation of dris reduction is... 

Why is this relevant to the diffusion of zinc in copper Imagine two adjacent lattice planes in the brass with two slightly different zinc concentrations, as shown in exaggerated form in Fig. 18.5. Let us denote these two planes as A and B. Now for a zinc atom to diffuse from A to B, down the concentration gradient, it has to squeeze between the copper atoms (a simplified statement - but we shall elaborate on it in a moment). This is another way of saying the zinc atom has to overcome an energy barrier... 

Staeking faults and sometimes proper polytypism are found in many inorganic compounds - to pick out just a few, zinc sulphide, zinc oxide, beryllium oxide. Interest in these faults arises from the present-day focus on electron theory of phase stability, and on eomputer simulation of lattice faults of all kinds investigators are attempting to relate staeking-fault concentration on various measurable character-isties of the compounds in question, such as ionicity , and thereby to cast light on the eleetronic strueture and phase stability of the two rival structures that give rise to the faults. 

Betyllium, because of its small size, almost invariably has a coordination number of 4. This is important in analytical chemistry since it ensures that edta, which coordinates strongly to Mg, Ca (and Al), does not chelate Be appreciably. BeO has the wurtzite (ZnS, p. 1209) structure whilst the other Be chalcogenides adopt the zinc blende modification. BeF2 has the cristobalite (SiOi, p. 342) structure and has only a vety low electrical conductivity when fused. Be2C and Be2B have extended lattices of the antifluorite type with 4-coordinate Be and 8-coordinate C or B. Be2Si04 has the phenacite structure (p. 347) in which both Be and Si... 

The predominantly ionic alkali metal sulfides M2S (Li, Na, K, Rb, Cs) adopt the antifluorite structure (p. 118) in which each S atom is surrounded by a cube of 8 M and each M by a tetrahedron of S. The alkaline earth sulfides MS (Mg, Ca, Sr, Ba) adopt the NaCl-type 6 6 structure (p. 242) as do many other monosulfides of rather less basic metals (M = Pb, Mn, La, Ce, Pr, Nd, Sm, Eu, Tb, Ho, Th, U, Pu). However, many metals in the later transition element groups show substantial trends to increasing covalency leading either to lower coordination numbers or to layer-lattice structures. Thus MS (Be, Zn, Cd, Hg) adopt the 4 4 zinc blende structure (p. 1210) and ZnS, CdS and MnS also crystallize in the 4 4 wurtzite modification (p. 1210). In both of these structures both M and S are tetrahedrally coordinated, whereas PtS, which also has 4 4... 

Figure 29.1 Crystal structures of ZnS. (a) Zinc blende, consisting of two, interpenetrating, cep lattices of Zn and S atoms displaced with respect to each other so that the atoms of each achieve 4-coordination (Zn-S = 235 pm) by occupying tetrahedral sites of the other lattice. The face-centred cube, characteristic of the cep lattice, can be seen — in this case composed of S atoms, but an extended diagram would reveal the same arrangement of Zn atoms. Note that if all the atoms of this structure were C, the structure would be that of diamond (p. 275). (b) Wurtzite. As with zinc blende, tetrahedral coordination of both Zn and S is achieved (Zn-S = 236 pm) but this time the interpenetrating lattices are hexagonal, rather than cubic, close-packed.

We have carried out impurity calculations for a zinc atom embedded in a copper matrix. We first perform self consistent band theory calculations on pure Cu and Zn on fee lattices with the lattice constant of pure Cu, 6.76 Bohr radii. This yields Fermi energies, self consistent potentials, scattering matrices, and wave functions for both metals. The Green s function for a system with a Zn atom embedded in a Cu matrix... 

The rate (or kinetics) and form of a corrosion reaction will be affected by a variety of factors associated with the metal and the metal surface (which can range from a planar outer surface to the surface within pits or fine cracks), and the environment. Thus heterogeneities in a metal (see Section 1.3) may have a marked effect on the kinetics of a reaction without affecting the thermodynamics of the system there is no reason to believe that a perfect single crystal of pure zinc completely free from lattic defects (a hypothetical concept) would not corrode when immersed in hydrochloric acid, but it would probably corrode at a significantly slower rate than polycrystalline pure zinc, although there is no thermodynamic difference between these two forms of zinc. Furthermore, although heavy metal impurities in zinc will affect the rate of reaction they cannot alter the final position of equilibrium. 

ZnO contauns excess metal which is accommodated interstitially, i.e. at positions in the lattice which are unoccupied in the perfect crystal. The process by which ZnO in oxygen gas acquires excess metal may be pictured as follows. The outer layers of the crystal are removed, oxygen is evolved, and zinc atoms go into interstitial positions in the oxide. We represent interstitial zinc by (ZnO). However, the interstitial zinc atoms may ionise to give (Zn O) or even (Zn O). The extra electrons produced in this way must occupy electron levels which would be vacant in the perfect crystal. We represent them by the symbol (eo), and refer to them as free electrons. They can be pictured as Zn ions at normal cation sites. We see therefore that three reactions can be written, each giving non-stoichiometric ZnO ... 

At each interface the interfacial potential will depend upon the chemical potentials of the species involved in the equilibrium. Thus at the Zn/Zn electrode there will be a tendency for zinc ions in the lattice to lose electrons and to pass across the interface and form hydrated ions in solution this tendency is given by the chemical potential of zinc which for pure zinc will be a constant. Similarly, there will be a tendency for hydrated Zn ions in solution to lose their hydration sheaths, to gain electrons and to enter the lattice of the metal this tendency is given by the chemical potential of the Zn ions, which is related to their activity. (See equation 20.155.) Thermodynamically... 

When the radius ratio of an ionic compound is less than about 0.4, corresponding to cations that are significantly smaller than the anion, the small tetrahedral holes may be occupied. An example is the zinc-blende structure (which is also called the sphalerite structure), named after a form of the mineral ZnS (Fig. 5.43). This structure is based on an expanded cubic close-packed lattice of the big S2 anions, with the small Zn2+ cations occupying half the tetrahedral holes. Each Zn2+ ion is surrounded by four S2 ions, and each S2" ion is surrounded by four Zn2+ ions so the zinc-blende structure has (4,4)-coordination. 

FIGURE 16.41 The atomic radii of copper and zinc are similar, and atoms of one element fit reasonably comfortably into the lattice of the other element to give the range of alloys that we know as brass. 

Homogeneous alloys of metals with atoms of similar radius are substitutional alloys. For example, in brass, zinc atoms readily replace copper atoms in the crystalline lattice, because they are nearly the same size (Fig. 16.41). However, the presence of the substituted atoms changes the lattice parameters and distorts the local electronic structure. This distortion lowers the electrical and thermal conductivity of the host metal, but it also increases hardness and strength. Coinage alloys are usually substitutional alloys. They are selected for durability—a coin must last for at least 3 years—and electrical resistance so that genuine coins can be identified by vending machines. 

Ziegler-Natta catalyst A stereospecific catalyst for polymerization reactions, consisting of titanium tetrachloride and triethylaluminum. zinc-blende structure A crystal structure in which the cations occupy half the tetrahedral holes in a nearly close packed cubic lattice of anions also known as sphalerite structure. 

The /3-alloys are different in nature from the 7-alloys and the a-manganese and /3-manganese structures discussed above, in that they are not complex structures, but are simple, being based upon the body-centered arrangement. /3-Brass, for example, has either a disordered structure, above 480°K, the copper and zinc atoms in essentially equal number being distributed largely at random over the points of a body-centered cubic lattice, or an ordered structure, below 300°K, with copper and zinc at the positions 000 and, respectively, of the cubic unit. Moreover, the physical properties of /3-brass are not those that indicate a filled zone structure. 

In connection with a discussion of alloys of aluminum and zinc (Pauling, 1949) it was pointed out that an element present in very small quantity in solid solution in another element would have a tendency to assume the valence of the second element. The upper straight line in Fig. 2 is drawn between the value of the lattice constant for pure lead and that calculated for thallium with valence 2-14, equal to that of lead in the state of the pure element. It is seen that it passes through the experimental values of aQ for the alloys with 4-9 and 11-2 atomic percent thallium, thus supporting the suggestion that in these dilute alloys thallium has assumed the same valence as its solvent, lead. 

Crystalline form cubic close pack (zinc blende) Lattice parameters a = 0.56531 O.nm... 

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