Valence strain index

The bond strain in this chapter, as in most other places in this book, is defined as the difference between the observed bond lengths and the bond lengths calculated from the theoretical bond valences. A bond strain index that measures this strain is defined in eqn (12.1). 

A more interesting index, but one more difficult to apply, is the bond strain index, B, which compares the observed and predicted bond valences by summing the squares of the deviation over all m bonds (24) ... 

Bond strain index Root mean square deviation between the observed and ideal bond valence averaged over all the bonds in the formula unit Bond valence, 5 The number of valence electrons an atom uses to form a given bond. In the ionic model it is equal to the electrostatic flux linking two ions. The... 

The lability of thieno[3,4-6]thiophene (3) and other iso-annelated systems, such as benzo[c]thiophene and benzole] furan, may be due to the strain effect (Mills-Nixon effect see also Zwanenburg et alP and references therein) in the condensed five-membered ring. The stability of the iso-annelated dithienothiophenes 7—9 is noteworthy. Simple LCAO MO method calculations on benzo[c]thiophene indicate that its instability is due to low specific delocalization energy and high free valence index at position 1. 

The predicted structures obtained by optimizing the bond valences of the ions have BVSs close to their formal valences. The degrees of freedom in the spinel structure enable the simultaneous optimization of the BVS for each of the A-, B-, and X-site ions. Within calculation limitations, a zero global instability index (G) is fotmd for each of the predicted structures. The experimentally determined structures have a larger G, ranging from about 0.04 to 0.27 v.u. with an average of 0.15 v.u. for the examined structures. Unlike the cubic perovskite and pyrochlore structure, the spinel is not a strained structure. Regardless of the sizes of the A and B... 

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