Previous methods for determining whether a uniform region of a sample is crystalline or isotropic—what we call the “state of internal orientation”

$\mathscr {S}$
S—require a prioriknowledge of properties of the purely crystalline and purely isotropic states. In addition, these methods can be ambiguous in their determination of state
$\mathscr {S}$
S
for particular materials and, for a given material, the spectral methods can be ambiguous when using particular peaks. Using first-principles Raman theory, we have discovered a simple, non-resonance, polarized Raman method for determining the state
$\mathscr {S}$
S
that requires no information a priori and will work unambiguously for any material using any vibrational mode. Similar to the concept behind “magic angle spinning” in NMR, we have found that for a special set of incident/analyzed polarizations and scattering angle, the dependence of the Raman modulation depth M on the sample composition—and, for crystalline regions, the unit cell orientation—falls out completely, leaving dependence on only whether the region is crystalline (M = 1) or isotropic (M = 0). Further, upon scanning between homogeneous regions or domains within a heterogeneous sample, our signal M is a clear detector of the region boundaries, so that when combined with methods for determining the orientations of the crystalline domains, our method can be used to completely characterize the molecular structure of an entire heterogeneous sample to a very high certainty. Interestingly, our method can also be used to determine when a given mode is vibrationally degenerate. While simulations on realistic terthiophene systems are included to illustrate our findings, our method should apply to any type of material, including thin films, molecular crystals, and semiconductors. Finally, our discovery of these relationships required derivations of Raman intensity formulas that are at least as general as any we have found, and herein we present our comprehensive formulas for both the crystalline and isotropic states.

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