Kinetics of Decelerated Melting

Abstract

Melting presents one of the most prominent phenomena in condensed matter science. Its microscopic understanding, however, is still fragmented, ranging from simplistic theory to the observation of melting point depressions. Here, a multimethod experimental approach is combined with computational simulation to study the microscopic mechanism of melting between these two extremes. Crystalline structures are exploited in which melting occurs into a metastable liquid close to its glass transition temperature. The associated sluggish dynamics concur with real-time observation of homogeneous melting. In-depth information on the structural signature is obtained from various independent spectroscopic and scattering methods, revealing a step-wise nature of the transition before reaching the liquid state. A kinetic model is derived in which the first reaction step is promoted by local instability events, and the second is driven by diffusive mobility. Computational simulation provides further confirmation for the sequential reaction steps and for the details of the associated structural dynamics. The successful quantitative modeling of the low-temperature decelerated melting of zeolite crystals, reconciling homogeneous with heterogeneous processes, should serve as a platform for understanding the inherent instability of other zeolitic structures, as well as the prolific and more complex nanoporous metal-organic frameworks.

Keywords: kinetics; melting; metal–organic frameworks; simulations; zeolites.

Figure 1

Decelerated melting of LSX (Na₁₉K₇₇Al₉₆Si₉₆O₃₈₄). a) Exemplary contour plot of in situ X‐ray diffraction data recorded during isothermal treatment at 780 °C. b) Structural location of the lattice planes used for evaluation. c) Crystallinity loss φ constructed from (a) using Equation (1). d) φ data fit to the kinetic model (Equation (2)), displaying individual fractions of LSX and LDA for melting at 780 °C. e,f) Arrhenius scaling of reaction times τ₁ and τ₂, the melt relaxation time of albite and carnegieite at T _m, melt viscosity (gray dots), and data extracted from pre‐melting of albite showing surface melting of a single lattice plane,34 with extrapolations of Arrhenius fits (dashed gray lines). f) Onset of melting, highlighting the different reaction timescales and the dominant phases LSX, LDA, and HDL (liquid) in time–temperature space. The darker‐shaded area in (f) indicates the experimental occurrence of carnegieite recrystallization according to ref. 32.

Figure 2

Structural signature of decelerated faujasite melting. a) Structural equivalence of quenched HDL and conventional glass from synchrotron XRD. b) Asymmetry ratio of Eu³⁺ photoluminescence with melting. c) Ex situ increase in ²⁹Si NMR linewidths with melting (top) and converse changes in the proportions of Si‐Al neighbors (bottom). d) Ex situ room temperature IXS with melting revealing a nonlinear decrease of the nonergodicity factor f ₀ (bottom) and an increase in the longitudinal sound velocity V _L (top). Arrows in (c) and (d) indicate the order–order LSX‐LDA (A) and the order–disorder LDA‐HDL transitions (B). e) Recovery of faujasite crystallinity over periods of years for material initially amorphized to 25, 75, 99, and 100%. f) Experimental (top) and computational data (bottom) showing the reversibility of the first reaction step of zeo‐LDA and LSX‐LDA, respectively. Data in (a) and (b) are from LSX and LSX Eu, respectively, data in (c)–(e) are from Na zeolite, and (f) are for silicalite and MD simulations—all exhibiting identical faujasite topology. Lines are to guide the eye.

Figure 3

Molecular dynamics simulation of silicalite amorphization. a) Schematic of the computational procedure. b–d) Detailed trajectories of the reaction progress on different superstructural scales, where each volume step represents a density increase of ≈0.089 g cm⁻³. Yellow and red balls in (b) and (c) represent silicon and oxygen ions, respectively. In (d), the evolution of the three fundamental building blocks is depicted, that is, a six‐membered ring, three edge‐sharing four‐membered rings, and the 12‐membered ring forming the faujasite cage.