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Raman Imaging of Str ess Patterns in Biomaterials   305


        draft of the confocal probe configuration and the laser penetration
        depths for 90 percent Raman emission in normal and confocal probe
        configurations are given in Fig. 10.1 and Table 10.1, respectively. In
        Table 10.1, penetration depth for Raman confocal and normal probe
          ∗
               ∗
        (z  and z , respectively) refres to the threshold depth value for 90 percent
          c    n
        Raman intensity emission. PS coefficients and data scatter recorded
        during calibration refer to the Raman band indicated in brackets.
   10.3  Raman Effect in Biological and
           Synthetic Biomaterials


        10.3.1 Spectral Features
        According to group theory, the phonon modes of solids decompose
        as irreducible representations, which split into selected vibrational
        modes. Such modes can be classified depending on the propagation
        direction of the selected mode with respect to the selected polariza-
        tion direction [(e.g., longitudinal optic (LO) or transverse optic (TO)].
        Selected Raman bands can be then used for stress assessments,
        according to the knowledge of their respective PS coefficients.
            Hydroxyapatite crystals possess a point group of C . The space
                                                       6
                6
        group  CP6(  ) specifies the unit cell symmetry for hydroxyapatite
                6  3
                           2
        more correctly than C ( P /m)6  , since the OH ions are not located on
                           6 h  3
                         22
        the mirror plane σ .  The phosphate and OH ions are located on sites
                        h
                                  6
        of C  and C  symmetries for C  space groups, respectively. The factor
            1     3               6
        group (or correlation) analysis based on these sites predicts types and
        numbers of symmetry species due to the crystal field splitting. It has
                                         6
        been reported that the space group of C  symmetry is consistent with
                                         6
        the results from the Raman experiments on synthetic hydroxyapatite
        at low temperature. Factor group analyses have been based on the
        following irreducible representation, with a total of five OH-
        related bands expected for space group of P6. 22
                                   +
                              Γ= AE   + E                    (10.1)
                                     1   2
            Figure 10.2 shows a typical spectrum of cortical bone (bovine
        femur), in which the pertinent vibrational modes has been labeled,
        although not all the theoretically predicted vibrational bands could
        be observed in the collected spectra.
            Alumina materials are of high-technological interest as synthetic bio-
        materials. They possess the corundum structure, which belongs to the
          6
                                                             23
        D  space group with two molecular Al O  groups per unit cell.  The
          3d                             2  3
        aluminum atoms are octahedrally coordinated with two layers of oxy-
        gen atoms, the octahedron being severely distorted. The irreducible rep-
        resentations for the optical modes in the crystal can be expressed as
                  Γ= 2A   + A2  + A3  + A2  + E5  + E4       (10.2)
                        1g    1u    2g    2u    g    u
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