Magnesium fluoride crystal structure

In order to specify the structure of a chemical compound, we have to describe the spatial distribution of the atoms in an adequate manner. This can be done with the aid of chemical nomenclature, which is well developed, at least for small molecules. However, for solid-state structures, there exists no systematic nomenclature which allows us to specify structural facts. One manages with the specification of structure types in the following manner magnesium fluoride crystallizes in the rutile type , which expresses for MgF2 a distribution of Mg and F atoms corresponding to that of Ti and O atoms in rutile. Every structure type is designated by an arbitrarily chosen representative. How structural information can be expressed in formulas is treated in Section 2.1. 

The Rutile Structure.—A large number of compounds MX crystallize with the tetragonal structure of rutile, TiCfe. In this structure the position of the ion X is fixed only by the determination of a variable parameter by means of the intensity of reflection of x-rays from various crystal planes. In accordance with the discussion in a following section, we shall assume the parameter to have the value which causes the distances between X and the three ions M surrounding it to be constant. With this requirement the inter-atomic distance R and the edges a and c of the unit of structure are related by the equation R = (a/4 /2) [2 + (c/o)2]. In this way the inter-atomic distances in Table XII are obtained. In the case of magnesium fluoride the agreement is satisfactory. 

With the aid of the data of Appendix F, predict the crystal structure of magnesium fluoride. (The observed structure is of the rutile type.)... 

Magnesium oxide and sodium fluoride have the same crystal structure as sodium chloride (shown in Fig. 4-5). Magnesium oxide has hardness 6 on the Mohs scale and sodium fluoride has hardness 3. Can you explain why the two substances differ so much in hardness Can you also explain why the melting point of magnesium oxide (2800 C) is very much higher than that of sodium fluoride (992 C) Note that the ions in the two substances have the same electronic structure. 

The factors which determine the reactivity of the limestone are not fully understood, but include the magnesium content, the aluminium and fluoride contents, and the crystal structure. The rate of reaction also depends on the particle size of the limestone. Thus, while a lower reactivity can be offset by finer grinding, it raises both operating and capital costs. Details of reactivity tests have been published, see [12.5,12.6]. 

The relative number of cations and anions also helps determine the most stable structure type. All the structures in Figure 12.27 have equal numbers of cations and anions. These structure types can be realized only for ionic compounds in which the number of cations and anions are equal. When this is not the case, other crystal structures must result. As an example, consider NaF, Mgp2, and SCF3 ( FIGURE 12.28). Sodium fluoride has the sodium chloride structure with a coordination number of 6 for both cation and anion. Magnesium fluoride has a tetragonal crystal structure called the rutile structure. The cation coordination number is stiU 6, but the fluoride coordination number is now only 3. In the scandium fluoride structure, the cation coordination number is stiU 6 but the fluoride coordination number has dropped to 2. As the cation/anion ratio goes down, there are fewer cations to surround each anion, and so the anion coordination number must decrease. We can state this quantitatively with the relationship... 

Of substances MX.j, silicon dioxide (radius ratio 0.29) forms crystals with tetrahedral coordination of four oxygen ions about each silicon ion, magnesium fluoride (radius ratio 0.48) and stannic oxide (radius ratio 0.51) form crystals with octahedral coordination of six anions around each cation (the rutile structure, Figure 18-2), and calcium fluoride (radius ratio 0.73) forms crystals with cubic coordination of eight anions around each cation (the fluorite structure. Figure 18-3). The ligancy (coordination number) increases with increase in the radius ratio, as indicated in Figure 18-1. 

Explain the following observations Magnesium oxide (MgO) and sodium fluoride (NaF) have the same crystal structure and approximately the same formula weight, but MgO is almost twice as hard as NaF. The melting points of MgO and NaF are 2852°C and 993°C, respectively. The boiling points of MgO and NaF are 3600°C and 1695°C, respectively. 

Goldschmidt predicted from his empirical rule that calcium chloride would not have the fluorite structure, and he states that on investigation he has actually found it not to crystallize in the cubic system. Our theoretical deduction of the transition radius ratio allows us to predict that of the halides of magnesium, calcium, strontium and barium only calcium fluoride, strontium fluoride and chloride, and barium fluoride, chloride,... 

Crystals of the intermetallic compound magnesium stannide, MgjSn, have been prepared and investigated by means of Laue and spectral photographs with the aid of the theory of space-groups. The intermetallic compound has been found to have the calcium fluoride structure, with dwo = 6.78 0.02 A. U. The closest approach of tin and magnesium atoms is 2.94 0.01 A. U. 

Fig. 13-11.—The structure of the cubic crystal KMgF3. Potassium ions are represented by large shaded circles. They are at the corners of the unit cube. The fluoride ions, represented by large open circles, are at the face-centered positions, and the magnesium ions, represented by small circles, are at the center of the cubes. This structure is often called the perovskite structure perovskite is the mineral CaTiOj.

Fluoride and hydroxide ions are saturated by bondB of total strength 1. This is achieved by two aluminum octahedral bonds, as in hydrar-gillite (Al(OH)t), with the structure shown in Figure 13-17, topaz (AljSiChF ), jmnyite, described below, and many other crystals, and also by three magnesium octahedra in brucite, Mg(OH)t, and other crystals. 

If we consider the fluorides, for example, which form pure coordination lattices (p. 33), then those from the alkaline earth metals with the exception of magnesium and beryllium crystallize in the fluorite structure, in which the cation is surrounded by eight fluorine ions for CaF2 and CdF2, which have the same structure, r+/r is 0.71 and 0.69 respectively just at the limit V 3— 1 — 0.73. The fluorides of other divalent ions, such as Mn, Fe, Co and Ni and also Mg, crystallize in a structure with coordination number six (rutile type). It is only for BeF2 that the ratio r+/r = 0.23 lies below the limit of this coordination number and it has a structure similar to that of cristobalite (Si02) with four neighbours (see also p. 66). 

Equation (53) describes Debye relaxation. Magnesium and calcium-doped lithium fluorides have a characteristic Debye relaxation diagram from vhich the dopant concentration and the relaxation time can be deduced. Many others crystals containing mobile lattice defects have similar Debye s relaxation processes. Major understanding of the structure of color centers results from dielectric relaxation spectra. Nuclear magnetic resonance, optical and Raman spectroscopy can be used efficiently in conjunction vith dielectric spectroscopy. 

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