A novel calorimetric approach and analytic method were proposed to characterize the glass transition and fragility of glass-forming systems. Initial characterization of the glass transition temperatures (onset, inflection, and end) was performed by precisely defining these points based on derivative behavior of the total heat flow curve obtained through differential scanning calorimetry (DSC). Geometric representation allowed for consolidation of critical glass transition data into one matrix. This glass transition matrix can be used for automated characterization of the regime, including thermodynamics and kinetics, via programmed computation. Comparison of results to traditional methods revealed excellent agreement with results derived by the novel procedure proposed, and indeed was corroborated by literature values of glass transition temperature, liquid fragility index, and activation energy. The proposed analytic methods establish a significant metrological traceability by development of a robust confidence interval for all targeted measurands, and in so doing provide a highly reproducible and efficient analysis via DSC. K E Y W O R D Scharacterization, calorimetry (or DSC), fragility (or liquid fragility index), glass transition, heat capacity How to cite this article: Mancini M, Sendova M, Mauro JC. Geometric analysis of the calorimetric glass transition and fragility using constant cooling rate cycles.

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Atomic structure dictates the performance of all materials systems; the characteristic of disordered materials is the significance of spatial and temporal fluctuations on composition−structure−property−performance relationships. Glass has a disordered atomic arrangement, which induces localized distributions in physical properties that are conventionally defined by average values. Quantifying these statistical distributions (including variances, fluctuations, and heterogeneities) is necessary to describe the complexity of glassforming systems. Only recently have rigorous theories been developed to predict heterogeneities to manipulate and optimize glass properties. This article provides a comprehensive review of experimental, computational, and theoretical approaches to characterize and demonstrate the effects of short-, medium-, and long-range statistical fluctuations on physical properties (e.g., thermodynamic, kinetic, mechanical, and optical) and processes (e.g., relaxation, crystallization, and phase separation), focusing primarily on commercially relevant oxide glasses. Rigorous investigations of fluctuations enable researchers to improve the fundamental understanding of the chemistry and physics governing glassforming systems and optimize structure−property−performance relationships for next-generation technological applications of glass, including damage-resistant electronic displays, safer pharmaceutical vials to store and transport vaccines, and lower-attenuation fiber optics. We invite the reader to join us in exploring what can be discovered by going beyond the average.

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The nonexponential relaxation behavior of glass is governed by the dimensionless stretching exponent, β, which is typically assumed to be a constant but is more accurately described as a function of temperature. Herein, relaxation calculations of glassy materials are undertaken via an iterative differential equationbased algorithm to determine when the use of a temperature-dependent (or dynamic) stretching exponent is required to capture the industrially relevant evolution of fictive temperature components, which is necessary for process engineering. Results reveal a range of liquid fragility index (m) in which a static β description is roughly equivalent to the behavior observed with a dynamic β. However, fast primary (α) relaxation modes demonstrate unique behavior in systems exhibiting excessively strong or fragile liquid behavior when a temperaturedependent stretching exponent is considered. In this special issue dedicated to the International Year of Glass, we also provide broader perspectives regarding the importance and impact of a temperature-dependent β.

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A direct, shape-and scale-independent digital image measurement method of the surface area (SA) of individual objects is proposed. The algorithms presented herein utilize the brightness histogram of 8-bit greyscale images, and thus are referred to as a brightness histogram surface area measurement algorithm (BHSAMA). The proposed SA measurement technique allows the uncertainty of the single measurement reading to be evaluated by traditional error propagation. Furthermore, the numerical value of the propagated uncertainty reflects the pixel brightness gradient of the edge pixels. This fact alone presents a significant advantage to the current methods utilizing image segmentation and/or edge detection whose measurement uncertainties cannot be quantitatively analysed. The proposed method does not involve any shape-related approximations. Five examples illustrating the method are discussed. For method verification purposes, a series of digital simulations using a control sample of predetermined size is undertaken. The accuracy of the single measured SA reading is between 0.5% and 1.5%. The uncertainty of the measured SA is evaluated and discussed further as a function of two types of simulated blurred edge region. The two presented BHSAMA techniques can have a wide range of applicability, from nanoparticles to cell biology to aerial imagery.