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As originally formulated by Phillips [1] for covalent networks, structural units are not considered in BCT. Instead, the system is viewed as a network of atoms at the vertices and covalent linear bonds at the edges. These covalent linear bonds provide r_i/2 linear constraints at the ith vertex of coordination number r_i. In addition, there also exist [r_i (d − 1) −d(d − 1)/2] covalent angular‐bond constraints at the ith vertex for a d‐dimensional network. The average number of constraints, n, per vertex is, therefore,

(10)

where r is the average vertex coordination number. The condition of isostaticity (n = d) gives the following value for the critical coordination number r* (also called the rigidity percolation threshold):

(11)

Note that r* = 2 for d = 2 and r* = 2.4 for d = 3. It must be emphasized that Eqs. (10) and (11) assume that the angular constraints are intact at every vertex. This assumption does not always hold true as illustrated by silica where the angular constraints at oxygens are broken, which is generally the case for elements that do not belong to groups III, IV, and V and do not exhibit sp⁽ⁿ⁾ hybridization.

Application of BCT to non‐covalent systems with long‐range interactions such as ionic systems is approximate at best, and questionable most of the time, because these systems do not lend themselves to the count of simple nearest‐neighbor constraint. For ionic systems, it is thus preferable to use PCT with structural units defined by the radius ratio of cations to anions.