The crystallization of a glass is a phase transformation of intense interest to materials scientists because it determines the thermal stability of amorphous materials used in phase-change memory devices, optical fibers, infrared optics, and solar cells. When a glass is held at a fixed temperature above its glass transition, tiny crystal nuclei form and grow until the entire sample has crystallized. The classical framework for describing this process is the Kolmogorov–Johnson–Mehl–Avrami (KJMA) model, which relates the fraction of material transformed at any moment, denoted α, to an exponential function of time raised to a power known as the Avrami exponent n, multiplied by a temperature-dependent rate constant k. According to the model, the transformed fraction follows α = 1 − exp(−(kt)^n), where k itself obeys Arrhenius behavior, k = A exp(−E/RT), with E the activation energy, A the Arrhenius prefactor, R the gas constant, and T the absolute temperature.

Traditionally, experimentalists determine these parameters by converting the raw DSC heat-flow signal into the extent of conversion as a function of time and then constructing double-logarithmic plots of ln[−ln(1 − α)] against ln t. This procedure, while effective, requires accurate knowledge of the moment at which crystallization begins—an assignment notoriously prone to error in isothermal experiments, where the sample takes time to equilibrate after being plunged into the hot furnace of the calorimeter. As Elabbar and Abu-Sehly emphasize, drawing on earlier insights from Waters and Paddy as well as Brown and Galwey, the relevant kinetic parameters can instead be derived directly from the shape of the DSC curve itself, sidestepping the conversion analysis entirely and potentially reducing experimental and numerical uncertainty.

The mathematical basis of the direct method is elegant. The DSC signal φ is proportional to the rate of transformation, φ = ΔHc·(dα/dt), where ΔHc is the total enthalpy released during crystallization, obtained from the area under the peak. Differentiating the KJMA expression yields a curve with a characteristic maximum at a time tmax given by tmax = (1/k)·[((n − 1)/n)]^(1/n). The height of the peak at that moment, φmax, combined with tmax and ΔHc, satisfies a simple relation involving only the Avrami exponent n. Thus, by measuring just the peak time, the peak height, and the total heat of crystallization, the researcher can solve for n, then back-substitute to obtain the rate constant k at each crystallization temperature. The method has one well-defined limitation: it does not apply to first-order reactions with n = 1, for which the DSC curve has no maximum.

Activation energy can likewise be obtained without conversion data. One route, developed previously by Elabbar and known as the Δt-method, uses the full width at half maximum of the crystallization peak. Plotting the natural logarithm of this width, Δt, against the reciprocal of the crystallization temperature Tc produces a straight line whose slope equals E/R. A second, newly demonstrated route exploits the position of the peak itself: because the half-crystallization time t1/2 of the conversion curve is closely related to tmax of the DSC peak, plotting ln tmax against 1/Tc also yields a straight line with slope E/R. Both approaches rely solely on geometric features of the calorimetric traces, making them insensitive to many of the ambiguities that plague conversion-based analyses.

To test the framework, the team prepared glassy In10Se90 by the melt-quenching technique. High-purity selenium and indium, each of five-nines purity, were sealed in evacuated quartz ampoules, heated to 950 °C for 24 hours with frequent rotation to ensure homogenization, and then rapidly quenched in water. Isothermal DSC measurements were performed on a TA Q2000 calorimeter under dry nitrogen, calibrated with indium standards, with a fixed 5-milligram sample mass. Crucially, the samples underwent a rejuvenation heat treatment to erase physical aging effects, ensuring that the crystallization kinetics reflected the intrinsic material rather than a history-dependent relaxation state.

The measurements delivered strikingly consistent numbers. For In10Se90 glass, the Δt-method gave an activation energy of 112 kJ/mol, a value widely reported in the literature for this composition. The new tmax method yielded 142 kJ/mol, while an Arrhenius plot of the directly determined rate constants gave E = 136 kJ/mol and an Arrhenius prefactor A of 3.22 × 10^16 s⁻¹. The Avrami exponent calculated from the peak analysis came out at approximately 2 across the crystallization temperatures studied. For the validation case of Sb10Se90, using data from an earlier study, the tmax method produced an activation energy of 98.9 kJ/mol, in excellent agreement with the 106 kJ/mol obtained by the Δt-method, while the Arrhenius treatment of the rate constants gave E = 105.6 kJ/mol and A = 4.81 × 10^11 s⁻¹—tight mutual confirmation across independent routes.

Beyond the numbers, the Avrami exponents reveal a fascinating physical story about how these two glasses crystallize. In In10Se90, an exponent near 2 points to a constrained growth mode—either one-dimensional growth with continuous nucleation or two-dimensional growth with a decreasing or limited nucleation rate—suggesting heterogeneous nucleation sites and anisotropic extension of crystalline domains within the amorphous matrix. In Sb10Se90, by contrast, an exponent near 3 signals three-dimensional, volumetric crystal growth proceeding uniformly through the bulk, under either constant nucleation or site-saturated nucleation. The substitution of antimony for indium thus fundamentally alters the geometry of the transformation, information that the direct DSC analysis captures with no additional experimental effort.

The authors note that the slightly different activation energies obtained from the different routes likely stem from an experimental artifact: the difficulty of assigning the true starting time t = 0 in isothermal DSC traces. The Δt-method is immune to this uncertainty because peak width, unlike peak position, does not depend on the choice of time zero, which is why the team argues it provides the most accurate estimates of E. Their conclusion that Δt-derived values agree best with the extensive literature supports this interpretation and offers practical guidance for anyone analyzing isothermal calorimetry data.

The broader significance of the work lies in accessibility. Isothermal DSC instruments are ubiquitous in materials laboratories, and the new method transforms what was once a multi-step fitting exercise into a set of straightforward measurements on the raw thermal traces—peak time, peak height, peak width, and total heat. For researchers designing chalcogenide glasses for phase-change memory, optical storage, or thermoelectric applications, this means faster, more reproducible characterization of thermal stability and crystallization behavior. It also reinforces a lesson that resonates across thermal analysis: sometimes the richest information about a material’s inner transformation is sitting in plain sight, in the very shape of the curve the instrument draws.

Subject of Research: Direct determination of crystallization kinetic parameters from isothermal DSC curves of chalcogenide glasses using the KJMA model

Article Title: Determination of the kinetic parameters for crystallization directly from isothermal DSC curves

Article References: Elabbar, A. A., & Abu-Sehly, A.-H. A. (2026). Determination of the kinetic parameters for crystallization directly from isothermal DSC curves. Discover Chemistry, 3(1), Article 503. https://doi.org/10.1007/s44371-026-00960-7

Image Credits: AI Generated

DOI: 10.1007/s44371-026-00960-7

Keywords: crystallization kinetics, differential scanning calorimetry, chalcogenide glasses, KJMA model, Avrami exponent, activation energy, isothermal DSC, thermal analysis, glass transition, In10Se90, Sb10Se90, Arrhenius equation