Crystal Structure-Free Method for Dielectric and Polarizability Characterization of Crystalline Materials at Terahertz Frequencies.

Terahertz (THz) time-domain spectroscopy provides a direct and nondestructive method for measuring the dielectric properties of materials directly from the phase delay of coherent electromagnetic radiation propagating through the sample. In cases when crystals are embedded within an inert polymeric pellet, the Landau, Lifshitz, and Looyenga (LLL) effective medium model can be used to extract the intrinsic dielectric constant of the crystalline sample. Subsequently, polarizability can be obtained from the Clausius-Mossotti (CM) relationship. Knowledge of the crystal structure density is required for an analytical solution to the LLL and CM relationships. A novel crystal structure-free graphical method is presented as a way to estimate both dielectric constants and polarizability values for the situation when the crystal structure density is unknown, and the crystals are embedded within a pellet composed of a non-porous polymer. The utility of this crystal structure-free method is demonstrated by analyzing THz time-domain spectra collected for a set of amino acids (L-alanine, L-threonine, and L-glutamine) embedded within pellets composed of polytetrafluoroethylene. Crystal structures are known for each amino acid, thereby enabling a direct comparison of results using the analytical solution and the proposed crystal structure-free graphical method. For each amino acid, the intrinsic dielectric constant is extracted through the LLL effective medium model without using information of their crystal structure densities. THz polarizabilities are then calculated with the CM relationship by using the determined intrinsic dielectric constant for each amino acid coupled with its crystal density as determined graphically. Comparison between the analytical and graphical solutions reveal relative differences between dielectric constants of 3.7, 5.1, and 13.6% for threonine, alanine, and glutamine, respectively, and relative differences between polarizability of 0.6, 0.9, and 5.4%, respectively. These values were determined over the 10-20 cm THz frequency range. The proposed method requires no prior knowledge of crystal structure information.