Magnesium pair potential

The resultant pair potentials for sodium, magnesium, and aluminium are illustrated in Fig. 6.9 using Ashcroft empty-core pseudopotentials. We see that all three metals are characterized by a repulsive hard-core contribution, Q>i(R) (short-dashed curve), an attractive nearest-neighbour contribution, 2( ) (long-dashed curve), and an oscillatory long-range contribution, 3(R) (dotted curve). The appropriate values of the inter-atomic potential parameters A , oc , k , and k are listed in Table 6.4. We observe that the total pair potentials reflect the characteristic behaviour of the more accurate ab initio pair potentials in Fig. 6.7 that were evaluated using non-local pseudopotentials. We should note, however, that the values taken for the Ashcroft empty-core radii for Na, Mg, and Al, namely Rc = 1.66, 1.39, and... 

Table 6.4 Pair potential parameters for sodium, magnesium, and aluminium at their equilibrium volumes. (From Pettifor and Ward...

Fig. 6.10 The phase shift, cc3, of the long-range contribution to the pair potential for sodium, magnesium, and aluminium as a function of their relative atomic volume, / ). (AfterWard (1985).)...

Fig. 6.12 The structure map, (Z, a3), that is predicted using the long-range pair potential,

Calculations of the interaction energy in very fine pores are based on one or other of the standard expressions for the pair-wise interaction between atoms, already dealt with in Chapter 1. Anderson and Horlock, for example, used the Kirkwood-Miiller formulation in their calculations for argon adsorbed in slit-shaped pores of active magnesium oxide. They found that maximum enhancement of potential occurred in a pore of width 4-4 A, where its numerical value was 3-2kcalmol , as compared with 1-12, 1-0 and 1-07 kcal mol for positions over a cation, an anion and the centre of a lattice ceil, respectively, on a freely exposed (100) surface of magnesium oxide. 

In contrast, for reaction of organic halides with metallic magnesium, Whitesides ( 7) found a poor correlation with the rates of tri-n-butyltin hydride, and a reasonable correlation, especially with primary bromides, with reduction potentials, suggesting the formation of RXT. Sodium naphthalene reductions also correlate with reduction potentials for primary halides (4b). Moreover, reaction rates are faster in solvents favoring loose ion pairs over tight, further evidence for an early transition state involving election transfer and little bond dissociation. (4c)... 

It is possible, but not yet proven, that the borate ion acts in a way similar to the sulfate ion. Like the sulfate anion, it does form soluble ion-pair complexes with calcium and magnesium ions and this may promote coadsorption on the chalk surface. However, in the absence of reliable data on borate ion adsorption and zeta potential data for chalk, it is difficult to confirm the mechanism behind the observed imbibition performance of borate. 

However, the magnesium half-reaction has the more negative electrode potential and therefore repels electrons more strongly and undergoes oxidation. The iron half-reaction has the more positive electrode potential and therefore attracts electrons more sdongly and undergoes reduction. So the reaction as written is not spontaneous. (The reaction pairs the reduction of Mg " with the reverse of a halfreaction above it in Table 18.1—such pairings are not spontaneous.)... 

Use standard reduction potentials to predict which metal in each of the following pairs is the stronger reducing agent under standard conditions (a) zinc or magnesium (b) sodium or tin. 

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