Figure 1 shows the calculated K_z+K_d for 26 compounds on the basis of the relationship in BOP assuming p∝Z^-c such as r_e=K_zln(Z)+C_z and r_e=K_dn(D_e/Z)+C_d where C, C_z, andC_d are the constants. Despite the values of K_z+K_d derived from the results of ZB and RS without G, this figure definitely reveals that the larger the K_z+K_d, the more stable the low-coordinated structures. Since large K_z+K_d is directly related to small r_e, small bond length is crucial for stabilizing low-coordinated structure such as G. In the range of Z≤4, however, the relation p∝Z^-c contradicts to ab initio results in Si obtained by Bazant and Kaxiras [3], who proposed p∝exp(-bZ²) instead of p∝Z^-c. Thus we reasonably employ the formula of p_Z≥4=(4/Z)^c at Z≥4 and p_Z≤4=aexp(-bZⁿ) at Z≤4, where c, a, b, and n are the parameters adjusted to reproduce D_e for G, ZB, and RS with conditions of d(p_Z≥4)/dZ=d(p_Z≤4)/dZ and p=1 at Z=4. The calculated bond order p₍₃₎ for Si (p₍₃₎=1.09) is favorably compared with the ab initio results (p₍₃₎=1.05) [3]. It is found that the values of p₍₃₎ of C, BN, and BeO are larger than those of Si consistent with the empirical Pauling relation r_e∝-ln(p). Moreover, comparing the ionicity f_i for each material with critical iconicity for the separation of threefold and fourfold-coordinated structures f_i^c(3-4)=3p₍₃₎²/(3p₍₃₎²+2Z_i²) estimated by electrostatic interactions between bond charges p and between ionic charges Z_i, graphitic structure G is favored in C and BN because of their f_i (0 for C and 0.143 for BN) smaller than f_i^c(3-4) (0.107 for C and 0.174 for BN) whereas WZ appears in BeO with its larger f_i (0.602) than f_i^c(3-4) (0.316). This is consistent with experimental findings where G does not appear in A ^N B^8-N compounds with N=2 . Consequently, bond length and ionicity are crucial for the structural stability of A^NB^8-N compounds so that the threefold-coordinated structure does not appear in II-VI and I-VII compounds with large iconicity but limitedly appear in the compounds with small r_e introducing large p₍₃₎ and small f_i such as C and BN.

References

[1] G. C. Abell, Phys. Rev. B 31 (1985) 6184.

[2] T. Ito, Jpn. J. Appl. Phys. 37 (1998) L1217.

[3] M. Z. Bazant and E. Kaxiras, Phys. Rev. B 56 (1997) 8542.  

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