Burns and Scott 17, 18 concluded that the peak maxima observed in the powder spectra match with those in the single crystals, illustrating their point by considering PbTiO 3 (PT) and Pb(Zr,Ti)O 3 (PZT) ceramics. Attempts to extract useful information from the Raman spectra collected from powders have been made already in the 70’s. In this case, the interpretation of the experiments is complicated by the fact that the observed Raman spectrum is, essentially, a superposition of the Raman spectra coming from several small crystallites (grains), each oriented in a different way, which often results in broad and asymmetric spectral features. More often the materials are produced in form of a powder or a polycrystal, e.g., ceramics. Unfortunately, it is not always possible to obtain single crystals. This procedure is possible because single crystals permit well-defined scattering geometries and the theory of Raman scattering in such materials is readily available. In the case of single crystals, the interpretation is greatly facilitated by group-theoretical considerations 3, 8 supported by first principles calculations of lattice dynamics 9, 10, 11, 12, 13, 14, 15, 16. The main difficulty when applying this technique and the obstacle to its further development, however, is the rather complicated interpretation of Raman spectra necessary for extracting relevant information about material properties. Hence, Raman spectroscopy has proven very effective for studying the strain state 4, defects 5, 6 and phase transitions 7 specifically in ceramics and semiconductors. can be determined by examining the Raman mode variations upon external stimuli or by compositional changes. Each phonon mode is associated to a specific atomic vibration (for example, stretching or breathing vibrations of chemical bonds or groups of atoms) that is sensitive to any geometry perturbation such that the influence of strain, temperature, electric field, etc. Raman spectra in crystals originate, mostly, from the interaction of lattice vibrations (phonons) with quanta of incident monochromatic radiation 1, 3. Its main advantages are higher spatial resolution compared to other laboratory-scale diffraction methods 2, relatively easy sample preparation, low cost, fast data acquisition, and the non-contact and non-destructive measurement capability that allows implementing in-situ and in-operando experimental methodologies. Raman spectroscopy is a powerful technique based on the inelastic scattering of light 1, which is being increasingly used as a tool for studying the local structure of materials. Additional advantages of the method are that it is general, permits automation, and thus can be used in high-throughput fashion. As exemplified by applying the method to rhombohedral BaTiO 3, AlN, and LiNbO 3, such an extension brings the simulated Raman spectrum to a much better correspondence with the experimental one. We start from the standard approach based on the (Placzek) rotation invariants of the Raman tensors and extend it to include the effect of the coupling between the lattice vibrations and the induced electric field, and the electro-optic contribution, relevant for polar materials like ferroelectrics. In this paper, we introduce a method for computing Raman spectra of polycrystalline materials from first principles. Whilst group theory considerations and standard ab initio calculations are helpful, they are often valid only for single crystals. Raman spectroscopy is an advantageous method for studying the local structure of materials, but the interpretation of measured spectra is complicated by the presence of oblique phonons in polycrystals of polar materials.
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