23 © 2017 Materials Research Society MRS BULLETIN • VOLUME 42 • JANUARY 2017 • www.mrs.org/bulletin Origin of glass-forming tendency Ever since the inception of academic glass research, practition- ers have often wondered—what is so special about the select few melts that can bypass crystallization and be supercooled to form bulk glasses at the glass-transition temperature ( T g )? With the important strides made in glass science in the past 35 years, both in theory and experiments, we now have a wealth of new information on the crucial role of network topology in decoding the origin of the glass-forming tendency. The Phillips–Thorpe Rigidity Theory 1–3 has been pivotal in elucidating the physics of network glasses. The key parame- ter in the theory is the number of constraints per atom, n c, , due to chemical bonds, in particular, bond-stretching and bond- bending interactions. When n c = 3, glassy networks are opti- mally constrained, fulfilling the Maxwell criteria for rigidity (i.e., n c = 3 for three-dimensional networks). Such optimally constrained networks within the Phillips–Thorpe approach possess a mean coordination number of 2.40. At n c < 3, net- works possess low-frequency floppy modes and are flexible, those with n c > 3, possess stress-creating redundant bonds and are stressed-rigid, while those with n c = 3 form networks that belong to an intermediate phase (IP). The comparative functionalities of the underlined three topological phases have evoked much interest in glass science. The first tests of these topology-driven ideas were applied to the chalcogenide glasses. These glasses represent alloys of Group VI (S, Se) elements with Group IV (Si, Ge) or Group V (P, As) elements. An attractive feature of these elements is that their chemical bonding conforms to the 8- N bonding rule, where N represents the number of valence electrons. Thus, the coordination number r acquired by Ge, As, and Se usually is 4, 3, and 2, respectively. One can thus enumerate the mechanical constraints per atom, n c , from a knowledge of the chemical stoichiometry alone of an alloyed glass composition such as Ge x As y Se 100–x–y . Thermally reversing windows and birth of the IP The most unusual nature of isostatically rigid networks came to the forefront when Raman scattering measurements and modulated differential scanning calorimetry (MDSC) experi- ments were performed in precise compositional studies of the chalcogenides. 4–6 Isostatically rigid networks are those in which optimally constrained local structures percolate across the glass sample. These experiments showed that IP networks do not form merely at one characteristic stoichi- ometry of r c = 2.40, but rather, over a small but finite range of connectivity, the IP window r c 1 < r < r c 2 , near 2.40, with sharply defined edges r c 1 and r c 2 representing the rigidity and stress transitions, respectively. To obtain such sharp edges, it is crucial that the alloyed melt/glass batch be highly homogeneous. 7 Within the IP window, glasses possess Glassy materials with enhanced thermal stability P. Boolchand and B. Goodman The nature of glass transitions in chalcogenides and modified oxides depends on the network mean coordination number r . These display systematic trends when spanning across the three topological phases: flexible, intermediate, and stressed-rigid. Trends in the glass-transition temperature T g ( r ) show a monotonic increase with r , but the nonreversing enthalpy of relaxation at T g , ΔH nr ( r ), shows a deep- and square-well-like minimum with the walls representing the rigidity and stress transitions with increasing r , respectively. In the well, the ΔH nr ( r ) term remains minuscule ( ∼0) corresponding to the isostatically rigid intermediate phase (IP). The melt fragility index ( m) shows rather low values, m( r ) < 20 for IP compositions, but increases outside the IP. Glass compositions in the IP show absence of network stress, form compacted networks, possess thermally reversing glass transitions, and display high glass-forming tendency—functionalities that have attracted widespread interest in understanding the physics of glasses and applications of the new IP formed. P. Boolchand, Department of ECS, College of Engineering and Applied Science, University of Cincinnati, USA; boolchp@ucmail.uc.edu B. Goodman, Department of Physics, University of Cincinnati, USA; goodman.bernard@gmail.com doi:10.1557/mrs.2016.300 https://www.cambridge.org/core/terms. https://doi.org/10.1557/mrs.2016.300 Downloaded from https://www.cambridge.org/core. University of Cincinnati Libraries, on 07 Feb 2019 at 14:41:23, subject to the Cambridge Core terms of use, available at