Lattices sodium chloride

We have already mentioned that for sodium chloride approximately 1.78 times as much energy is released when the crystal lattice forms as when ion pairs form. This value, the Madelung constant (A) for the sodium chloride lattice, could be incorporated to predict the total energy released when 1 mole of NaCl crystal is formed from the gaseous Na+ and Cl- ions. The result would be... 

Potassium fluoride crystallizes in a sodium chloride lattice. The length of the edge of the unit cell (sometimes called the cell or lattice constant) has the value 267 pm for KF. 

KBr crystallizes in a sodium chloride lattice arrangement with a cell edge length of 314 pm. 

We now introduce a Fourier transform procedure analogous to that employed in the solution theory, s 62 For the purposes of the present section a more detailed specification of defect positions than that so far employed must be introduced. Thus, defects i and j are in unit cells l and m respectively, the origins of the unit cells being specified by vectors R and Rm relative to the origin of the space lattice. The vectors from the origin of the unit cell to the defects i and j, which occupy positions number x and y within the cell, will be denoted X 0 and X for example, the sodium chloride lattice is built from a unit cell containing one cation site (0, 0, 0) and one anion site (a/2, 0, 0), and the translation group is that of the face-centred-cubic lattice. However, if we wish to specify the interstitial sites of the lattice, e.g. for a discussion of Frenkel disorder, then we must add two interstitial sites to the basis at (a/4, a/4, a]4) and (3a/4, a/4, a/4). (Note that there are twice as many interstitial sites as anion-cation pairs but that all interstitial sites have an identical environment.) In our present notation the distance between defects i and j is... 

The structure-dependent coefficients have been calculated for the three primitive cubic lattices.4 For the sodium chloride lattice we have A — 2a3, where a denotes the anion-cation lattice spacing, and if we define a parameter bi by the equation... 

Let us restrict further discussion to the case of equal and opposite charges on a sodium chloride lattice and use the definitions... 

The series 6 - 12/21/2 + 8/31/2 - 6/41/2 + 24/51/2 -. .. eventually becomes convergent and gives the value for the Madelung constant for the sodium chloride lattice (the standard description of lattices which have the same form as that adopted by sodium fluoride). The values of Madelung constants for some common crystal lattices are given in Table 7.5. 

The sodium chloride structure. Sodium chloride crystallizes in a face-centered cubic structure (Fig. 4.1a). To visualize the face-centered arrangement, consider only the sodium ions or the chloride ions (this will require extensions of the sketch of the lattice). Eight sodium ions form the comers of a cube and six more are centered on the faces of the cube. The chloride ions are similarly arranged, so that the sodium chloride lattice consists of two interpenetrating face-centered cubic lattices. The coordination number (C.N.) of both ions in the sodium chloride lattice is 6. that is, there are six chloride ions about each sodium ion and six sodium ions about each chloride ion. 

Now in the crystal lattice there will be more interactions than the simple one in an ion pair. In the sodium chloride lattice, for example, there are attractions to the six nearest neighbors of opposite charge, repulsions by the twelve next nearest neighbors of like charge, etc. The summation of all of these geometrical interactions is known as the Modelling constant, A. The energy of a pair of ions in the crystal is then ... 

In the same way we can predict that sodium ions will prefer octahedral holes m a closest packed lattice of chloride ions (rNB Acr 116 pm/167 pm = 0.69), forming the well-known sodium chloride lattice with a coordination number of 6 (Fig. 4.1a). 

Sulfide compounds are formed by all of the Group IVA elements, and lead is found as the sulfide in its principle ore galena that has Pb2+ and S2 ions in a sodium chloride lattice (see Chapter 3). A chain structure is shown by SiS2 in which each Si is surrounded by four S atoms in an approximately tetrahedral environment ... 

The structure of MnO consists of discrete Mn2+ and O2- ions in a sodium chloride lattice. 

AgF, AgCl and AgBr crystallize with a sodium chloride lattice and CuCl, CuBr, and Cul with the lattice given in Figure 62 in which copper has a coordination number of four. This difference in crystal structure of the two salts is not determined by the difference in the dimensions of the Ag"+ and Cu+ ions, since according to Pauling the latter has the value 0-96 A, which is not outside the limits for a sodium chloride lattice. The decrease of the coordination number from six to four and the formation of a tetrahedral configuration are more probably determined by the covalent character of the bonds between copper and chlorine. However, it is to be emphasized that the bonds are not entirely covalent any more than they are entirely ionic, but are of an intermediate... 

The oxides of the alkaline earth metals crystallize in a sodium chloride lattice although in SrO and BaO the radius ratio is greater than 0 732. It has been proposed that the crystals are constructed from the ions M + and the electron affinity of the oxygen atom calculated on this assumption by the Born-Haber cycle for the different oxides give rather... 

The type of lattice is not always determined by the radius ratio. For example, the ratio of the ionic radii in GaS and GdS is identical (0 53) but nevertheless GaS crystallizes in a sodium chloride lattice and GdS in a zinc sulphide type. Similar behaviour is observed with the corresponding tellurides. For sulphur, nitrogen and their analogues where the valency state of nitrogen is... 

This compound is a liquid at room temperature, that is to say it has a much lower melting point than sodium chloride. It follows that the forces holding together the sodium chloride lattice must be stronger than the forces holding together the particles of the solid in a carbon tetrachloride lattice. The particles of the carbon tetrachloride are individual molecules of CCU the particles of the sodium chloride are charged ions all... 

The sodium chloride lattice. The smaller spheres are Na+ the larger are Cl. ... 

Sodium chloride lattice, 89 Solid solubility, calculation of, 1 IS —, effect of temperatuiv on, 00, 74, 75... 

Mercuric sulfide, HgS, is precipitated from aqueous solutions as a black, highly insoluble compound. The solubility product is 10 54, but the sulfide is somewhat more soluble than this figure would imply because of some hydrolysis of Hg2+ and S2- ions. The black sulfide is unstable with respect to a red form identical with the mineral cinnabar and changes into it when heated or digested with alkali polysulfides or mercurous chloride. The red form has a distorted sodium chloride lattice with Hg—S chains similar to those in HgO. Another form, occurring as the mineral metacinnabarite, has a zinc blende structure, as have the selenide and telluride. 

Europium (II) sulfide is a black powder possessing a sodium chloride lattice and an unknown melting point. Crystals of the sulfide have a golden hue by reflected light. The compound exhibits ferromagnetism with a Curie temperature of 17°K. Above this temperature, europium (II) sulfide behaves as a typical paramagnetic compound. ... 

The studies of Australian and English students suggest that many think that each ion in the sodium chloride lattice could only form one bond. This relates to the full shells explanatory principle that students use to explain bonding a sodium atom is considered to need to donate one electron (and therefore forms one bond) and a chlorine atom is seen to need to gain one electron (forming one bond). The bond would therefore (according to students) only exist between ions that had transferred electrons. From this explanation students obviously get the idea that a single bond is formed - not a network or a lattice (Taber, 1997, 1998). 

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