Computational Modeling for Phononic Crystal Property Discovery and Design – From Eigenvalue Analysis to Machine Learning

Phononic crystals are artificially engineered materials that can forbid phonon propagation in a specific frequency range that is referred to as a “phononic band gap.” Phononic crystals that have band gaps in the GHz to THz range can potentially enable sophisticated control over thermal transport with “phononic devices”. Calculations of the phononic band diagram are the standard method of determining if a given phononic crystal structure has a band gap. However, calculating the phononic band diagram is a computationally expensive and time-consuming process that can require sophisticated modeling and coding. In addition to this computational burden, the inverse process of designing a phononic crystal with a specific band gap center frequency and width is a challenging problem that requires extensive trial-and-error work.

In this dissertation, I first present colloidal nanocrystal superlattices as a new class of three-dimensional phononic crystals with periodicity in the sub-20 nm size regime using the plane wave expansion method. These calculations show that colloidal nanocrystal superlattices possess phononic band gaps with center frequencies in the 102 GHz range and widths in the 101 GHz range. Varying the colloidal nanocrystal size and composition provides additional opportunities to fine-tune the phononic band gap. This suggests that colloidal nanocrystal superlattices are a promising platform for the creation of high frequency phononic crystals.

For the next topic, I explore opportunities to use supervised machine learning for expedited discovery of phononic band gap presence, center frequency and width for over 14,000 two-dimensional phononic crystal structures. The best trained model predicts band gap formation, center frequencies and band gap widths, with 94% accuracy and coefficients of determination (R2) values of 0.66 and 0.83, respectively.

Lastly, I expand the above machine learning approach to use machine learning to design a phononic crystal for a given set of phononic band gap properties. The best model could predict elastic modulus of host and inclusion, density of host and inclusion, and diameter-to-lattice constant ratio for target center and width frequencies with coefficients of determinations of 0.94, 0.98, 0.94, 0.71, and 0.94 respectively. The high values coefficients of determination represents great opportunity for phononic crystal design.