Abstract
A combined quantum-mechanical and thermodynamic approach to the mechanical properties of multicomponent silicate glasses is presented. Quantum chemical calculations based on density-functional theory (DFT) on various silicate systems were performed to explore the crystalline polymorphs existing for a given chemical composition. These calculations reproduced the properties of known polymorphs even in systems with extensive polymorphism, like MgSiO3. Properties resting on the atomic and electronic structure, i.e., molar volumes (densities) and bulk moduli were predicted correctly. The theoretical data (molar equilibrium volumes, bulk moduli) were then used to complement the available experimental data. In a phenomenological evaluation, experimental data of bulk moduli, a macroscopic property resting on phononic structure, were found to linearly scale with the ratios of atomic space demand to actual molar volume in a universal way. Silicates ranging from high-pressure polymorphs to glasses were represented by a single master line. This suggests that above the Debye limit (in practice: above room temperature), the elastic waves probe the short range order coordination polyhedra and their next-neighbor linkage only, while the presence or absence of an extended translational symmetry is irrelevant. As a result, glasses can be treated – with respect to the properties investigated – as commensurable members of polymorphic series. Binary glasses fit the very same line as their one-component end-members, again both in the crystalline and glassy state. Finally, it is shown that the macroscopic properties of multicomponent glasses also are linear superpositions of the properties of their constitutional phases (as determined from phase diagrams or by thermochemical calculations) taken in their respective glassy states. This is verified experimentally for heat capacities and Young’s moduli of industrial glass compositions. It can be concluded, that the combined quantum mechanical and thermochemical approach is a truly quantitative approach for the design of glasses with desired mechanical properties, e.g., for the development of high-modulus glasses.
Highlights
Elastic properties of glasses have gained great importance during the last years
Theoretical bulk moduli and equilibrium molar volumes were obtained by fitting the electronic energies at several well-chosen volumes to Murnaghan’s equation of state (Murnaghan, 1937)
The starting structures were taken from the literature and the molar volume was varied and the structure was optimized with fixed volume and symmetry
Summary
Elastic properties of glasses have gained great importance during the last years. Especially for reinforcement applications it is essential to develop glass compositions with targeted elastic moduli. Elastic Moduli of Silicate Glasses very successful in general, but are applicable to very limited compositional regions only. This is due to the fact that glasses typically are extremely non-ideal mixtures if described on the basis of their oxide components j. As previously shown (Conradt, 2004), glasses can be treated as nearly ideal mixtures of components reflecting the stoichiometries of their coexisting constitutional compounds k. In this description frame, heats of mixing and (due to the number of atoms comprised in each k) even entropies of mixing may be neglected. The close relation of this stoichiometric concept to structural reality has been demonstrated by NMR and neutron scattering experiments (Vedishcheva et al, 2001; Wright et al, 2001)
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