In crystalline solids several types of vibration may occur. In addition to acoustic modes, two main types are identified, “internal vibrations” associated with molecules and molecular ions with covalent bonds that are present in the solid and “external vibrations” corresponding to the vibrations of species and ions in their crystallographic site [2–4]. Internal vibrations are generally close to the vibration energy of the free molecule/ions and allow the identification of molecular species in the solid. However, variations will appear in the energies of internal vibrations and in their relative intensities which depend on the environments of these molecular species in the solid. Such variations allow a precise identification of mineral structures in most cases. Although external vibration modes also depend on the crystal structure, their energy is lower than that of internal vibrations, and they are more easily accessed using Raman spectroscopy. Among these external vibrations, two types of movements may be recognized: translation modes and libration modes, which can be viewed as partial rotation of molecular groups in the crystal. Libration movements of OH⁻ ions and H₂O molecules occur at a relatively high energy compared to non-protonated molecules, and the corresponding lines are frequently found among the internal vibrations of other species like phosphate or carbonate. To complete the description of vibrational spectra, overtone and combination lines, which involve multi-quanta excitations, can be observed, although with much weaker intensities than fundamental lines.

The main molecules and molecular ions found in calcium phosphates are orthophosphate groups: PO₄ ³⁻, HPO₄ ²⁻, and also H₂O, OH⁻, CO₃ ²⁻. The vibrational characteristics of the “free” CO₃ ²⁻ and PO₄ ³⁻ ions are shown in Table 8.1 [5, 6], with the symmetry group and vibrational domains. We will use the denominations of the spectroscopic domains of the free molecules/ions to describe and discuss the different spectra in this paper. Although specific domains can be used for protonated phosphate species [5, 7], the P–O vibrational regions remain close to those of the PO₄ ³⁻ group and they will be discussed by reference to this ion. In protonated species additional lines are expected due to the O–H bond. The stretching of the O–H bonds in HPO₄ ²⁻ and groups are generally broad and appear with a low to medium intensity. However, the P-(OH) bonds in HPO₄ ²⁻ and are longer and weaker than the P–O bond in the PO₄ ³⁻ ion, and the corresponding stretching bands are shifted towards lower wavenumbers. These bands are very sensitive to hydrogen bonding [5, 8, 9]. In contrast the weakening of the P–OH bond is associated with a strengthening of the remaining P–O bonds, whose stretching vibrations are shifted towards higher wavenumbers, whereas bending vibrations are shifted towards lower wavenumbers. The symmetry alterations induced by protonation occurring in HPO₄ ²⁻ can conveniently be described using distorted PO₄ edifices belonging to C_3v symmetry (although the symmetry of the real free ions is lower). These species have been included in Table 8.1.

The vibrational modes of “free” molecular ions and molecules are conveniently determined using molecular group theory [1], which is used to name and distinguish the vibrational modes. Group theory also allows determination of the infrared (IR) and Raman (R) observance of the vibrational modes, their “activity,” which is related to the physical interactions between electromagnetic radiations and vibrational energy levels involved in these spectroscopic methods [2–4].

In crystalline solids two main alterations have been identified: the site symmetry effect and the factor group symmetry [2–4]. The site symmetry effect corresponds to an alteration in vibrational energy levels due to the symmetry lowering of the “free” molecule or polyatomic ion related to its position in a well-defined crystallographic site; these effects are shown in Tables 8.2, 8.3, and 8.4 for different crystalline calcium phosphates in different structures [5, 9–14]. Considering PO₄ ³⁻ ions in apatites with a hexagonal unit cell (space group P6₃/m; Table 8.3), for example, the site symmetry is C_s, as only a symmetry plane is preserved from the original tetrahedral symmetry. In consequence, the degeneracy of vibrational modes E (degeneracy: 2) and T₂ (degeneracy: 3) of the “free” PO₄ ³⁻ species is raised, and instead of one vibrational level, several non-degenerated modes occur. All these vibrational modes are active in IR and R and a “splitting” of the ν₂, ν₃, and ν₄ lines is predicted. In addition, ν₁ and ν₂ modes are now active in IR, although they were not observed for the free ion.

The factor group treatment provides a complete prediction of the vibrational levels of a crystal for both internal and external vibration modes. This approach takes into consideration the whole content of the unit cell, including the correlations between the vibrations of similar groups in a crystal that may interfere with each other in a confined environment. These considerations result in additional vibrational levels of molecules and molecular ions as shown in Tables 8.2, 8.3, and 8.4. The number of predicted lines may vary considerably according to the structure. For compounds containing HPO₄ ²⁻, OH⁻ ions, and water molecules, line broadenings are observed related to hydrogen bonding. In addition, libration transitions, which have not been considered here, appear in addition to bending and stretching lines.

The factor group may lead to weak shifts so, when numerous lines are expected, individual components are hindered by line broadening and cannot be distinguished. Molecular group theory, site symmetry, and factor group treatments do not allow the prediction of spectra with their line positions and intensities.

This information can be provided by quantum chemistry calculations [15]. For mineral structures with disordered or partially occupied sites and for solid solutions, factor group theory is more difficult to apply. For amorphous structures like amorphous calcium phosphates, the spectra prediction may rely on the symmetry of basic structural units, Posner’s clusters (Table 8.5) [16], although the S₆ symmetry of these clusters has been discussed and lower symmetry, C₁ or C₃, has been proposed depending on the environment [17].