Chemical Medium-Range Order Enables Stoichiometric Rigidity

TL;DR

This study investigates the structural origins of rigidity in covalent glasses near the Maxwell threshold, emphasizing the crucial role of medium-range order (MRO) over other factors.

Contribution

It demonstrates that medium-range order (MRO) proxies are essential for understanding rigidity, surpassing enthalpic stress, defects, and geometric linking density.

Findings

Enthalpic stress delays rigidity onset.

Chemical defects are insufficient to explain rigidity.

MRO proxies successfully recover rigidity at realistic strengths.

Abstract

Maxwell counting predicts an isostatic threshold at $\langle r\rangle = 2.4$ for covalent network glasses, but which structural correlations actually produce rigidity near this point is still unclear. In this work, we test four candidates: enthalpic stress, chemical defects, geometric interlocking, and medium-range order (MRO). We use a locally tree-like configuration model as a zero-MRO baseline and apply perturbations to test each candidate. We find that (i) enthalpic stress delays rigidity rather than enabling it; (ii) chemical defects require fractions ($\sim$40%) far above experimental values ($\sim$16% in GeSe$_2$); (iii) geometric linking density does not govern the threshold location, which is instead set by loop-induced redundancy; and (iv) only phenomenological MRO proxies recover rigidity at experimentally accessible strengths. Consequently, chalcogenide intermediate-phase data and amorphous SiO$_2$ ring statistics positively implicate chemical MRO, while DNA spatial networks independently rule out pure geometric entanglement. We conclude that rigidity near the Maxwell threshold requires chemistry-specific correlations beyond pure connectivity.