Configurational Order–Disorder in Aluminosilicate Zeolite Frameworks

Abstract

Al placement in aluminosilicate zeolite frameworks, treated as a Löwenstein-constrained “framework gas” of Si and Al on the T-site network, is investigated using Wang–Landau sampling. For composition Si1–fAlf (0 ≤ f ≤ 1/2), bipartite-graph frameworks with all even-membered rings, such as faujasite (FAU), undergo two structural phase transitions as f increases. At fcpFAU ≳ 0.21 (Si:Al ≈ 3.8), a graph-theoretic analog of critical opalescence emerges, in which ordered Al clusters metastably compete between the antiphase bipartite subgraphs. At fcFAU ≳ 0.31 (Si:Al ≈ 2.2), the system undergoes an order–disorder transition, where one subgraph dominates, analogous to an Ising ferromagnet crossing Tc. Ordering completes at fmaxFAU = 1/2 (Si:Al = 1) in one of the two bipartite states. Nonbipartite frameworks with moderate odd-ring densities (e.g., MFI) frustrate subgraph ordering but exhibit the same qualitative behavior, with ordering competing among the symmetry-related saturated states at fmax < 1/2. Frameworks dominated by odd rings (e.g., MTN, 94% 5-rings) are too frustrated to sustain either transition. Above fc, Al ordering in bipartite frameworks is combinatorially inevitable, dictated by graph topology under Löwenstein’s rule alone, independent of framework energetics or synthesis conditions. Random dense packing of Al in FAU already reaches f ≈ 0.36 ± 0.05, well within the ordered regime, and exhibits substantial medium-range order despite the randomness of Al insertions.