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 0 K. 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.

Thermal expansion mechanism of cordierite with titanium or germanium doping based on ab initio molecular dynamics simulation

“…It appears to be difficult to evaluate the high-temperature region accurately because the thermal fluctuation is large compared with the low-temperature region, and the crystal structure may deviate significantly. The previous theoretical study of the thermal expansion of cordierite 24 using the anharmonic approach also had the problem of reproducing the experimental result in the high-temperature region-the simulation of the high-temperature region may be the application limit of the ab initio approach (See also the other MD simulation papers 25,26 ). Nevertheless, the simulation successfully reproduced the experimental result under 600 K, and the negative thermal expansion of the caxis, and we therefore consider that it is feasible to apply AIMD to investigate the thermal expansion of cordierite.…”

“…The recent phonon analysis by Li et al 24 shows quite reasonable agreement with experimental CTE within the moderate temperature region, whereas the vibration approach sometimes has difficulty in reproducing the high-temperature region because vibration analysis tends to underestimate the entropy effect. An alternative approach is classical molecular dynamics (MD), and three types of MD simulations have been reported [25][26][27] to investigate the ionic size effect on thermal expansion mechanism. Although these MD simulations can qualitatively reproduce the experimental thermal expansion, the NTE mechanism has not yet been elucidated.…”

“…For this purpose, Si in cordierite is replaced with Ti or Ge, and the ab initio MD simulation (AIMD) is performed to predict the CTE. Although Tokizono et al 25 attempted to perform an AIMD in cordierite, there was some discrepancy with the experimental result. Thus, it is worthwhile performing a pure cordierite simulation with AIMD to investigate whether the simulation result can reproduce the experimental result.…”