Zinc radii

It is noteworthy that the Be—O distance (1.60 A) is of the same order as that found for other coordination compounds of beryllium and leads to the value of 1.0—1.1 A for the covalent radius of beryllium in this type of coordination.26 Clearly arguments based on relative ionic radii are invalid. Thus the dihydrate of zinc oxinate has been shown to form a distorted tetrahedron with two long Zn—H20 bonds while the lengths Zn—O and Zn—N to the ligand are 2.05 and 2.06 A respectively, whence the zinc radius is 1.38 A. Clearly the use of an ionic radius (Zn2+ = 0.74 A) would be misleading. Similarly the Cu—N bond in compounds of Cu11 with ammonia and ethylenediamine (1.99,2.05,2.01 A) implies a radius of 1.3-1.4 A in these coordination compounds, a value considerably larger than the ionic radius of 0.7 A.23... 

Fig. 3J0 Plot of cumulative pore volume against logarithm of r the effective pore radius, (o) For charcoal AY4 A by mercury intrusion O by capillary condensation of benzene, (b) For zinc chloride carbon AYS A by mercury intrusion O by capillary condensation of benzene x by capillary condensation of benzene, after mercury intrusion followed by distillation of mercury under vacuum at temperature rising to 350°C. (Courtesy...

The most common oxidation state of niobium is +5, although many anhydrous compounds have been made with lower oxidation states, notably +4 and +3, and Nb can be reduced in aqueous solution to Nb by zinc. The aqueous chemistry primarily involves halo- and organic acid anionic complexes. Virtually no cationic chemistry exists because of the irreversible hydrolysis of the cation in dilute solutions. Metal—metal bonding is common. Extensive polymeric anions form. Niobium resembles tantalum and titanium in its chemistry, and separation from these elements is difficult. In the soHd state, niobium has the same atomic radius as tantalum and essentially the same ionic radius as well, ie, Nb Ta = 68 pm. This is the same size as Ti ... 

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. 

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. 

After rising at copper and zinc, the curve of metallic radii approaches those of the normal covalent radii and tetrahedral covalent radii (which themselves differ for arsenic, selenium, and bromine because of the difference in character of the bond orbitals, which approximate p orbitals for normal covalent bonds and sp3 orbitals for tetrahedral bonds). The bond orbitals for gallium are expected to be composed of 0.22 d orbital, one s orbital, and 2.22 p orbitals, and hence to be only slightly stronger than tetrahedral bonds, as is indicated by the fact that R(l) is smaller than the tetrahedral radius. 

Dullenkopf, 1936 Riederer, 1936 Fink Willey, 1937 Little, Raynor Hume-Rothery, 1943). The approximate composition Mg3Zn3Al2 was assigned to the phase, which extends over a wide range of values of the Zn/Al ratio. The atomic percentage of magnesium is nearly constant for the alloys, as would be expected from the fact that the metallic radius of magnesium is about 15% greater than those of aluminum and zinc. 

Approximate atomic coordinates were obtained by assuming the effective metallic radius of magnesium to be about 1-60 A and the radii of aluminum and zinc to be about 1-40 A. The corresponding calculated structure factors were in fairly good agreement with those obtained from the observed intensities. The preliminary atomic coordinates are given in Table 1. 

For sphalerite and wurtzite, for example, the discussion of partial ionic character as described above for molyde-nite leads to the resultant average charges +0.67 for sulfur and—0.67 for zinc. The distribution of the sulfur atoms is calculated to be 12% S2 (quadricovalent), 50 percent S+, 32 percent S°, 6 percent S-, 0.2% S2-. The observed bond length 2.34 A with the sulfur radius 1.03 A and the Schomaker-Stevenson correction 0.05 A leads to 5 = 1.36 A for zinc (quadricovalent Zn2-). The increase by 0.05 A over the value 1.309 A for sp3 bonds of Zn° is reasonable as the result of screening of the nucleus by the extra electrons. 

For compounds of the composition MX (M = cation, X = anion) the CsCl type has the largest Madelung constant. In this structure type a Cs+ ion is in contact with eight Cl-ions in a cubic arrangement (Fig. 7.1). The Cl- ions have no contact with one another. With cations smaller than Cs+ the Cl- ions come closer together and when the radius ratio has the value of rM/rx = 0.732, the Cl- ions are in contact with each other. When rM/rx < 0.732, the Cl- ions remain in contact, but there is no more contact between anions and cations. Now another structure type is favored its Madelung constant is indeed smaller, but it again allows contact of cations with anions. This is achieved by the smaller coordination number 6 of the ions that is fulfilled in the NaCl type (Fig. 7.1). When the radius ratio becomes even smaller, the zinc blende (sphalerite) or the wurtzite type should occur, in which the ions only have the coordination number 4 (Fig. 7.1 zinc blende and wurtzite are two modifications of ZnS). 

The electrostatic part of the lattice energy for chlorides crystallizing in the CsCl, NaCl and zinc blende type as a function of the radius ratio... 

The zinc blende type is unknown for truly ionic compounds because there exists no pair of ions having the appropriate radius ratio. However, it is well known for compounds with considerable covalent bonding even when the zinc blende type is not to be expected according to the relative sizes of the atoms in the sense of the above-mentioned considerations. Examples are CuCl, Agl, ZnS, SiC, and GaAs. We focus in more detail on this structure type in Chapter 12. 

Figure 7-3. Active site properties of CAII from SCC-DFTB/MM-GSBP simulations [91]. (a) The root mean square differences between the RMSFs calculated from GSBP simulations (WT-20 and WT-25 have an inner radius of 20 and 25 A respectively) and those from Ewald simulation, for atoms within a certain distance from the zinc, plotted as functions of distance from the zinc ion that die center of die sphere in GSBP simulations is the position of the zinc ion in the starting (crystal) structure, (b) The diffusion constant for TIP3P water molecules as a function of the distance from the zinc ion in different simulations...

The zinc +2 ion, with its six-coordinate radius of 0.74 A, is almost identical in size to both the magnesium (0.72) and the copper (0.73) ions, but zinc is much more polarizing than the alkaline earth metal and consequently has a well-defined, albeit limited, coordination chemistry. In keeping with the much lower hardness of Zn2+ (77 = 10.88 eV) versus Mg2+ (32.55 eV),9 zinc has a much greater affinity for softer ligands than magnesium, a fact that is also reflected in the natural occurrence of zinc as sulfide ores. 

There are two forms of zinc sulfide that have structures known as wurtzite and zinc blende. These structures are shown in Figures 7.7a and 7.7b. Using the ionic radii shown in Table 7.4, we determine the radius ratio for ZnS to be 0.39, and as expected there are four sulfide ions surrounding each zinc ion in a tetrahedral arrangement. Zinc has a valence of 2 in zinc sulfide, so each bond must be 1/2 in character because four such bonds must satisfy the valence of 2. Because the sulfide ion also has a valence of 2, there must be four bonds to each sulfide ion. Therefore, both of the stmctures known for zinc sulfide have a tetrahedral arrangement of cations around each anion and a tetrahedral arrangement of anions around each cation. The difference between the structures is in the way in which the ions are arranged in layers that have different structures. 

The reversible half wave potential ( 1/2) values became higher with the increase of the concentration of supporting electrolyte, but the a values were practically constant. The rate parameters decreased with increase of radius and charge of the cation of supporting electrolyte at the same ionic strength. The number of water molecules associated with zinc ions in the solutions and with reactant, which directly takes part in the charge-transfer process, was estimated and the following reaction scheme was proposed. 

Fig. 2.1. A lens for high-resolution acoustic microscopy in reflection. The central transparent part is a single crystal of sapphire, with its c-axis accurately parallel to the axis of the cylinder. The sandwich structure at the top is the transducer, with the yellow representing an epitaxially grown layer of zinc oxide between two gold electrodes. The pink shaded areas within the sapphire represent the plane-wavefronts of an acoustic pulse they are refracted at the lens cavity so that they become spherical in the coupling fluid. A lens for use at 2 GHz would have a cavity of radius 40f[Pg.8]

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