Tian Series Covalency and Bond Length

Tian and co-workers [71-73] developed an atomistic model to connect the bulk modulus of various crystals to the parameters of bond order, length, and polarity, which has reproduced the measured bulk moduli of a series of polar covalent crystals. Although conceptually similar to the BOLS correlation, they presented more appreciably with much details to various simations to form the series. 

They calibrated the bond strength in covalent and ionic crystals by using the effectively bonded valence electron (EVBE) number, Mab. of a chemical bond, which can be used as a parameter to characterize the bond type 

For single-bond crystals, the normalized bond volume, v = n, cf /Q, can be used as a measure of crystal geometry, where Ub, d, and Q are the bond number in the unit cell, bond length, and unit ceU volume, respectively [74]. Both the EVBE number and the coordination number product can easUy be calculated for a designated crystal, which also apphes to multi-bond crystals. 

Three main parameters affecting the bulk modulus, i.e., the bond length d), EVBE number ( ab), and coordination number product (p = ma b). are determined. The empirical expression for bulk modulus is deduced for simple type covalent crystals with one coordination number. The generalization to covalent crystals with diverse coordination numbers and ionic crystals are presented sequentially, followed by generalization to multi-bond crystals. 

Monocovalent crystals. The single-bond A B type covalent crys- 

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