Sodium atomic structure

Figure Bl.8.4. Two of the crystal structures first solved by W L Bragg. On the left is the stnicture of zincblende, ZnS. Each sulphur atom (large grey spheres) is surrounded by four zinc atoms (small black spheres) at the vertices of a regular tetrahedron, and each zinc atom is surrounded by four sulphur atoms. On the right is tire stnicture of sodium chloride. Each chlorine atom (grey spheres) is sunounded by six sodium atoms (black spheres) at the vertices of a regular octahedron, and each sodium atom is sunounded by six chlorine atoms.

The archetype of the ionic ceramic is sodium chloride ("rocksalt"), NaCl, shown in Fig. 16.1(a). Each sodium atom loses an electron to a chlorine atom it is the electrostatic attraction between the Na ions and the CF ions that holds the crystal together. To achieve the maximum electrostatic interaction, each Na has 6 CF neighbours and no Na neighbours (and vice versa) there is no way of arranging single-charged ions that does better than this. So most of the simple ionic ceramics with the formula AB have the rocksalt structure. 

The structure of the low-temperature modification of the compound, Na2Ta205F2 (I), has not yet been determined. The high-temperature modification, Na2Ta205F2 (II), can be conceived as two sub-lattices Tai6X52, which is composed of TaX6 octahedrons and Na Xt, which contains Na X2 tetrahedrons [192]. Fig. 38 shows the structure of Na2Ta205F2 (II). Two additional sodium atoms occupy the centers of two bi-pyramids with distorted hexagonal bases. 

The experimental values for the lithium halides are high. This is due to two different phenomena. In the case of the chloride, bromide and iodide the anions are in mutual contact, that is, the repulsive forces operative are those between the anions, and the anion radius alone determines the inter-atomic distances. The geometry of the sodium chloride structure requires that, for less than 0.414, the anions come into contact... 

The elucidation of the factors determining the relative stability of alternative crystalline structures of a substance would be of the greatest significance in the development of the theory of the solid state. Why, for example, do some of the alkali halides crystallize with the sodium chloride structure and some with the cesium chloride structure Why does titanium dioxide under different conditions assume the different structures of rutile, brookite and anatase Why does aluminum fluosilicate, AljSiCV F2, crystallize with the structure of topaz and not with some other structure These questions are answered formally by the statement that in each case the structure with the minimum free energy is stable. This answer, however, is not satisfying what is desired in our atomistic and quantum theoretical era is the explanation of this minimum free energy in terms of atoms or ions and their properties. 

There seem to be many binary metallic systems in which there are phases of this sort. In the sodium-lead system there are two such phases. One of them, based on the ideal structure Na3Pb, extends from 27 to 30 atomic percent lead, with its maximum at about 28 atomic percent lead and the other, corresponding to the ideal composition NaPb3, extends from 68 to 72 atomic percent lead, with maximum at about 70 atomic percent. The intensities of X-ray reflection have verified that in the second of these phases sodium atoms occupy the positions 0, 0, 0, and the other three positions in the unit cell are occupied by lead atoms isomorphously replaced to some extent by sodium atoms (Zintl Harder, 1931). These two phases are interesting in that the ranges of stability do not include the pure compounds Na8Pb and NaPb3. 

The brittleness of these intermetallic compounds suggests an electronic structure involving a filled Brillouin zone. It was pointed out by Ketelaar (1937) that the strongest reflection, that of form 531, corresponds to a Brillouin polyhedron for which the inscribed sphere has a volume of 217 electrons per unit cube, which agrees well with the value 216 calculated on the assumption that the sodium atom is univalent and the zinc atoms are bivalent that is, calculated in the usual Hume-Rothery way. It has also been... 

Galena, PbS, has the sodium chloride structure, with ligancy 6 for each atom. The Pb-S distance is 2.968 A. A possible structure is that based on the normal sulfur atom... 

Figure 6. Schematic projection and tunnel structure of BaTi40g(a) and NagTieOiaCb). O.oxygen atom .titeinium atom barium or sodium atom X. center of gravity of six oxygen ions. The arrows indicate the dipole moments.

Assume that the iron atoms in the crystal are in a perfect array, identical to the metal atoms in the sodium chloride structure, and that the 0.058 excess of oxygen is due to interstitial oxygen atoms being present, over and above those on the normal anion positions. The unit cell of the structure now contains 4 Fe and (4 x 1.058) O. The density is calculated to be 6076 kg m-3. 

Assume that the oxygen array is perfect and identical to the nonmetal atom array in the sodium chloride structure and that the unit cell contains some vacancies on the iron positions. In this case, one unit cell will contain 4 atoms of oxygen and (4/1.058) atoms of iron, that is, 4Feo.94sO. The density is calculated to 5741 kg m-3. 

Nickel oxide, NiO, which adopts the sodium chloride structure (Fig. 1.14), can readily be made slightly oxygen rich, and, because the solid then contains more oxygen than nickel, the crystal must also contain a population of point defects. This situation can formally be considered as a reaction of oxygen gas with stoichiometric NiO, and the simplest assumption is to suppose that the extra oxygen extends the crystal by adding extra oxygen sites. Atoms are added as neutral atoms, and... 

Cadmium oxide, CdO, like nickel oxide, also adopts the sodium chloride structure (Fig. 1.14). However, unlike nickel oxide, this compound can be made to contain more metal than oxygen. The defects that cause this metal excess are usually considered to be interstitial Cd atoms or ions. In this case the reaction is one in which the solid formally loses oxygen. Because of the rules of equation writing, this must involve the removal of neutral oxygen atoms. Each oxygen lost results in the loss of a nonmetal site. In order to keep the site ratio correct, a metal site must also be lost, forcing the metal into interstitial sites ... 

The nature of a surface will depend upon which atoms are exposed. For example, the surface of a crystal with the sodium chloride structure might consist of a mixture of atoms, as on 100 (Fig. 3.34a), or of just one atom type, as on 111 (Fig. 3.34b and 3.34c). However, it must be remembered that no surface is clean and uncontaminated unless it is prepared under very carefully controlled conditions. Absorbed gases, especially water vapor, are invariably present on a surface in air, which leads to changes in chemical and physical properties. 

The most stable cluster consists of an aggregation of four cation vacancies in a tetrahedral geometry surrounding an Fe3+ ion, called a 4 1 cluster. Cations in the sodium chloride structure normally occupy octahedral sites in which each metal is coordinated to six nonmetal atoms. The central Fe3+ ion in the 4 1 cluster is displaced into a normally unoccupied tetrahedral site in which the cation is coordinated to four oxygen ions. Because tetrahedral sites in the sodium chloride structure are normally empty, the Fe3+ is in an interstitial site. Equation (4.1) can now be written correctly as... 

Figure 5.20 Energy barriers during atomic diffusion (a) an atom diffusing in a sodium chloride structure or similar passes through octahedral and tetrahedral sites separated by triangular bottlenecks and (b) a schematic energy barrier with a periodicity equal to a, rising to a maximum when the diffusing atom has to pass a bottleneck between two stationary atoms.

The structure in Figure 2.14 shows the result of an ionic reaction sodium metal has reacted with chlorine gas to yield white crystalline sodium chloride, NaCl. Each Na atom has lost an electron to form an Na+ cation and each chlorine atom has gained an electron and is hence a CP anion. In practice, the new electron possessed by the chloride came from the sodium atom. 

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