Mechanical and Thermo-Mechanical properties of Materials
Die Theorie der thermischen Ausdehnung geht über 80 Jahre auf Arbeiten von Born (1923) und Grüneisen zurück, und erfordert eine Berechnung der Phononenfrequenzen und ihre Veränderungen mit Änderungen in der Größe der Einheitszelle. Dies ist eine große Herausforderung, selbst wenn man nur wenige Atome in der Zelle hat, und unsere Erklärung der thermischen Ausdehnung in ß-Eukryptit ist wirklich bemerkenswert. Die Hochtemperatur-Struktur von ß-Eukryptit (Abbildung) hat 21 Atome in der Einheitszelle, und die Struktur bei niedriger Temperatur hat sogar 84 Atome in der Zelle!
The main constituent of the CERAN cooking tops of the company Schott is the alumino-lithia-silica glass ceramic beta-eucryptite, which has a very small thermal expansion coefficient over a temperature range of around 1000 degrees. For the crystalline form of beta-eucryptite (see figure, oxygen atoms are green, lithium atoms are brown, silicon atoms blue, and aluminium atoms red), density functional calculations - which are free of adjustable parameters show that the thermal expansion coefficients parallel and at right angles to the lithium chains are almost constant. The coefficient parallel to the chains is negative and twice as large as the positive coefficient normal to the chains, and a polycrystalline sample should have a constant and very small thermal expansion. Since the atomic movements can also be followed in a precise way, it is possible to understand the reasons for this behaviour.
It is interesting to ask whether simpler and numerically less demanding theories can reproduce experimental measurements, and whether they can work in crystals that are not isotropic and/or close-packed. Several groups have been working on calculations of elastic constants, and it is generally accepted that they can be calculated with a quite reasonable precision. Many other challenges remain, including the calculation of the various entropic contributions to the free energy and the theoretical description of P-V-T diagrams. There is cause for optimism, although one must never forget that approximations are unavoidable in DF calculations.
( R. O. Jones, J. Harris)