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⁻¹ THz frequency range. The proposed method requires no prior knowledge of crystal structure information.

太赫兹（THz）时域光谱仪提供了一种直接且无损的方法，用于直接从传播通过样品的相干电磁辐射的相位延迟中测量材料的介电性能。如果将晶体包埋在惰性聚合物颗粒中，则可以使用Landau，Lifshitz和Looyenga（LLL）有效介质模型来提取晶体样品的固有介电常数。随后，可从克劳修斯-莫索蒂（CM）关系获得极化率。对于LLL和CM关系的解析解决方案，需要具有晶体结构密度的知识。提出了一种新颖的无晶体结构图形方法，用于估算未知晶体结构密度时的介电常数和极化率值，晶体被包埋在由无孔聚合物组成的颗粒中。这种无晶体结构方法的实用性通过分析THz时域光谱来证明，该光谱是针对嵌入在由聚四氟乙烯组成的颗粒中的一组氨基酸（L-丙氨酸，L-苏氨酸和L-谷氨酰胺）收集的THz时域光谱。每种氨基酸的晶体结构都是已知的，因此可以使用分析溶液和建议的无晶体结构的图形方法直接比较结果。对于每种氨基酸，通过LLL有效介质模型可以提取其固有介电常数，而无需使用其晶体结构密度的信息。然后，通过使用每种氨基酸的测定的固有介电常数和以图形方式确定的其晶体密度，以CM关系计算THz极化率。分析和图形解决方案之间的比较表明，苏氨酸，丙氨酸和谷氨酰胺的介电常数之间的相对差异分别为3.7、5.1和13.6％，极化率的相对差异分别为0.6、0.9和5.4％。这些值是在10–20 cm范围内确定的^-1 THz频率范围。所提出的方法不需要晶体结构信息的先验知识。