Reinhard Conradt is a retired professor from RWTH Aachen University, Germany. He has been performing glass research at Fraunhofer Institute of Silicate Science, ISC Würzburg, Germany, for six years, then served for ten years as university lecturer and industry consultant in an emerging market of Asia (Thailand). For the past 20 years, he was full professor and Chair of Glass & Ceramic Composites at RWTH Aachen University, Germany. Since 2015, he has been serving as President of the German Society of Glass Technology DGG.
Relation between Glass Structure and Thermodynamic Properties
Science and Technology of Glass uniglassAC GmbH, Nizzaallee 75, 52072 Aachen, GERMANY
At the atomic scale, a glass is characterized by the absence of translational order. At the microscale, a glass is a homogeneous and isotropic material characterized by the absence of any internal phase boundaries. Thus, different from most other materials, its properties cannot be designed via micro-structure. Rather, its macroscopic properties are determined primarily by its chemical composition, and to a lesser extent by the path of glass formation (typically: its cooling history). A continued challenge consists in understanding the relation between the structure of a glass and its macroscopic properties. Technologically, the challenge consists in rendering such understanding useful to the design of glasses with desired properties.
The present contribution focuses on macroscopic properties resting on phononic states, i.e., on the nature of atomic vibrations and elastic waves. These are, first, the properties derived from the heat capacity cP, in specific: enthalpy, entropy, and Gibbs energy. The heat capacity is related to vibrations with thermal frequencies ƒ in the order of ƒ = kT/h. Above room temperature, cP is determined by short-range order (SRO; i.e., the nature of cation coordination polyhedra) alone. The presence or absence of translational atomic order does not play any role. This suggests that, on spatial average, one-component glasses and their iso¬chemical crystalline counterparts typically exhibit identical SRO. This observation is extended to the liquid state as well as to multicomponent systems. Glasses differ from the isochemical crystalline systems by small amounts Hvit and Svit only. As a result, a quantitative thermochemical description of glasses and glass melts is obtained allowing one to treat any reactions involving a glass or a glass melt as reaction partner at an accuracy level fully sufficient for techno¬logical purposes. Typical examples are the energy demand of glass melting and chemical durability. Fig. 1 demonstrates the degree of accuracy with the cP(T) function of a standard float glass. The approach is extended to rheology. Fig. 2. shows an Adam-Gibbs analysis of the viscosity-tempera¬ture function of the same glass. The Adam-Gibbs parameters cP/Svit calculated thermochemically and derived from melt fragility agree very well; cP denotes the heat capacity jump in the glass transition.
Fig. 1. Heat capacity of standard float glass DGG-1, experimental vs. calculated data
Fig. 2. Adam-Gibbs analysis of viscosity data of standard float glass DGG-1
In contrast to the heat capacity, the elastic properties are determined by elastic waves in the acoustic range. Such waves probe both the short-range order (SRO) and the medium-range order (MRO; i.e., the nature of linkage among the cation-anion polyhedral) of a glass. It is shown that one-component glasses behave like low-density polymorphs of a given composition. Again, the presence or absence of translational atomic order does not play any role. For multi-component systems, the macroscopic elastic properties are obtained from a linear superposition of MRO entities the stoichiometry of which is determined from the constitutional phases of the polycrystalline state. This is supported by ab-initio DFT calculations. Fig. 3a shows, for the example of MgSiO3, how the bulk moduli of crystalline polymorphs and the glass scale with the atomic packing density. The linear superimposition principle is demonstrated in Fig. 3b for the binary series (CaMg)Si2O6 – (NaAl)Si2O6. Here pC denotes the per¬colation limit at which the bulk modulus vanishes. It agrees well with pC =0.43 for corner-linked tetrahedral structures.
Fig. 2. Bulk modulus vs. atomic packing density; one-component (a.) and a binary (b.) series of
The above observations go together well with Frenkel’s statement that, in view of the small energetic and entropic differences, the structures of crystals and their isochemical glasses and liquids cannot be dramatically different.