Sodium lattice

Figure 1.15 Energy band diagram for a sodium lattice. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc. After J. C. Slater, Phys. Rev., 45, 794 (1934).

S = Heat of sublimation of sodium D = Dissociation energy of chlorine / = Ionization energy of sodium = Electron affinity of chlorine Uq = Lattice energy of sodium chloride AHf = Heat of formation of sodium chloride. 

An indirect estimate of surface tension may be obtained from the change in lattice parameters of small crystals such as magnesium oxide and sodium chloride owing to surface tensional compression [121] however, these may represent nonequilibrium surface stress rather than surface tension [68]. Surface stresses may produce wrinkling in harder materials [122]. 

The BCC structure is illustrated in figure Al.3,3. Elements such as sodium, tungsten and iron fonn in the BCC structure. The conventional unit cell of the BCC structure is cubic, like FCC, with the length of the edge given by the lattice parameter, a. There are two atoms in the conventional cell. In the primitive unit cell, there is only one atom and the lattice vectors are given by... 

The rocksalt stmcture is illustrated in figure Al.3.5. This stmcture represents one of the simplest compound stmctures. Numerous ionic crystals fonn in the rocksalt stmcture, such as sodium chloride (NaCl). The conventional unit cell of the rocksalt stmcture is cubic. There are eight atoms in the conventional cell. For the primitive unit cell, the lattice vectors are the same as FCC. The basis consists of two atoms one at the origin and one displaced by one-half the body diagonal of the conventional cell. 

A/ij the lattice energy of sodium chloride this is the heat liberated when one mole of crystalline sodium chloride is formed from one mole of gaseous sodium ions and one mole of chloride ions, the enthalpy of formation of sodium chloride. 

To date there is no evidence that sodium forms any chloride other than NaCl indeed the electronic theory of valency predicts that Na" and CU, with their noble gas configurations, are likely to be the most stable ionic species. However, since some noble gas atoms can lose electrons to form cations (p. 354) we cannot rely fully on this theory. We therefore need to examine the evidence provided by energetic data. Let us consider the formation of a number of possible ionic compounds and first, the formation of sodium dichloride , NaCl2. The energy diagram for the formation of this hypothetical compound follows the pattern of that for NaCl but an additional endothermic step is added for the second ionisation energy of sodium. The lattice energy is calculated on the assumption that the compound is ionic and that Na is comparable in size with Mg ". The data are summarised below (standard enthalpies in kJ) ... 

Although the data for the silver halides suggest that silver(I) fluoride is likely to be more soluble than the other silver halides (which is in fact the case), the hydration enthalpies for the sodium halides almost exactly balance the lattice energies. What then is the driving force which makes these salts soluble, and which indeed must be responsible for the solution process where this is endothermic We have seen on p. 66 the relationship AG = — TAS and... 

After firing, the powder is washed in water typically with a small amount of complexing agent such as ethylenediarninetetraacetic acid (EDTA), sodium EDTA, or a weak acid such as citric acid to remove the excess chloride, volatile antimony oxychlorides which have recondensed on the phosphor during cooling, and manganese compounds which are not incorporated in the halophosphate lattice. The powder is then ready for suspension. 

Only body-centered cubic crystals, lattice constant 428.2 pm at 20°C, are reported for sodium (4). The atomic radius is 185 pm, the ionic radius 97 pm, and electronic configuration is lE2E2 3T (5). Physical properties of sodium are given ia Table 2. Greater detail and other properties are also available... 

The Group 1 elements are soft, low-melting metals which crystallize with bee lattices. All are silvery-white except caesium which is golden yellow "- in fact, caesium is one of only three metallic elements which are intensely coloured, the other two being copper and gold (see also pp. 112, 1177, 1232). Lithium is harder than sodium but softer than lead. Atomic properties are summarized in Table 4.1 and general physical properties are in Table 4.2. Further physical properties of the alkali metals, together with a review of the chemical properties and industrial applications of the metals in the molten state are in ref. 11. 

Reaction of [Rh(/z-Cl)(CO)2]2 with sodium pyrazolate leads to 206 (85CJC699). The Rh2N2Cl ring has the envelope conformation. The rhodium atom has distorted square-planar coordination. The molecules in the crystalline lattice form onedimensional stacking units with alternating rhodium atoms in the binuclear units, intermolecularly interacting in a zigzag chain. 

Values of the distance of closest approach derived from experimental values of the activity coefficients are given in column 2 of Table 40. It will be seen that for the lithium and sodium salts the value is greater than the crystal-lattice spacing (given in column 4) by rather more than 1 angstrom, as is expected. For the salts of cesium, rubidium, and potassium, on the other hand, the distance of closest approach... 

As a result of these effects, anions in general are larger than cations. Compare, for example, the Cl- ion (radius = 0.181 nm) with the Na+ ion (radius = 0.095 nm). This means that in sodium chloride, and indeed in the vast majority of all ionic compounds, most of the space in the crystal lattice is taken up by anions. 

In the sodium chloride crystal, the Na+ ion is slightly too large to fit into holes in a face-centered lattice of Cl- ions (Figure 9.18). As a result, the Cl- ions are pushed slightly apart so that they are no longer touching, and only Na+ ions are in contact with Cl- ions. However, the relative positions of positive and negative ions remain the same as in LiCk Each anion is surrounded by six cations and each cation by six anions. 

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. 

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