Theoretical approaches for studying anisotropic negative thermal expansion: A case of cordierite

Abstract

First-principles approaches on reproduction of negative and anisotropic thermal expansion of ceramics were examined. We have tested quasi-harmonic free-energy calculation and molecular dynamics (MD) simulation including lattice change based on the density functional theory. For intuitive understanding, a classical force-field MD was also applied. As a test case, we have chosen cordierite, which is particularly important for recent application for electronic precision components, catalytic converter for automobile exhaust gas, and is known to show negative and anisotropic thermal expansion at a certain region of temperatures. Quasi-harmonic free-energy approach showed appearance of negative expansion of cordierite in certain temperatures, while the anisotropy was not reproduced. We conclude this may be due to lack of anisotropic lattice change throughout the optimization of the unit cell and internal coordinates under hydrostatic pressures at 0K. On the other hand, MD simulation allowing lattice change showed anisotropy of a-, b-axes and c-axis of cordierite while the negative expansion region in temperature was not found, which may be due to limitation of available size of unit cell. Furthermore, by performing classical force-field MD, we found that local chemical-bond nature is a key in understanding the behavior of the cordierite under finite temperatures. From current simulated results, we propose necessity of intensive works to compare theoretical work with future accessible experiments using single-crystal samples.