Analytical and Bioanalytical Chemistry

, Volume 407, Issue 12, pp 3325–3342 | Cite as

Vibrational algorithms for quantitative crystallographic analyses of hydroxyapatite-based biomaterials: I, theoretical foundations

  • Giuseppe PezzottiEmail author
  • Wenliang Zhu
  • Marco Boffelli
  • Tetsuya Adachi
  • Hiroaki Ichioka
  • Toshiro Yamamoto
  • Yoshinori Marunaka
  • Narisato Kanamura
Research Paper


The Raman spectroscopic method has quantitatively been applied to the analysis of local crystallographic orientation in both single-crystal hydroxyapatite and human teeth. Raman selection rules for all the vibrational modes of the hexagonal structure were expanded into explicit functions of Euler angles in space and six Raman tensor elements (RTE). A theoretical treatment has also been put forward according to the orientation distribution function (ODF) formalism, which allows one to resolve the statistical orientation patterns of the nm-sized hydroxyapatite crystallite comprised in the Raman microprobe. Close-form solutions could be obtained for the Euler angles and their statistical distributions resolved with respect to the direction of the average texture axis. Polarized Raman spectra from single-crystalline hydroxyapatite and textured polycrystalline (teeth enamel) samples were compared, and a validation of the proposed Raman method could be obtained through confirming the agreement between RTE values obtained from different samples.


Hydroxyapatite Polarized Raman spectroscopy Crystallographic analyses Tooth enamel 


  1. 1.
    Schaeberle MD, Morris HR, Turner JF II, Treado PJ (1999) Peer reviewed: Raman chemical imaging spectroscopy. Anal Chem 71:175A–181ACrossRefGoogle Scholar
  2. 2.
    Kneipp K, Kneipp H, Itzkan I, Dasari RR, Feld MS (1999) Ultrasensitive chemical analysis by Raman spectroscopy. Chem Rev 99:2957–2976CrossRefGoogle Scholar
  3. 3.
    Tu AT (2003) Use of Raman spectroscopy in biological compounds. J Chin Chem Soc 50:1–10Google Scholar
  4. 4.
    Peticolas WL (1975) Application of Raman spectroscopy to biological macromolecules. Biochimie 57:417–428CrossRefGoogle Scholar
  5. 5.
    Penel G, Leroy G, Rey C, Bres E (1998) MicroRaman spectral study of the PO4 and CO3 vibrational modes in synthetic and biological apatites. Calcif Tissue Int 63:475–481CrossRefGoogle Scholar
  6. 6.
    Nishino M, Yamashita S, Aoba T, Okazaki M, Moriwaki Y (1981) The laser-Raman spectroscopic studies on human enamel and precipitated carbonate-containing apatites. J Dent Res 60:751–755CrossRefGoogle Scholar
  7. 7.
    Kravitz LC, Kingsley JD, Elkin EL (1968) Raman and infrared studies of coupled PO4 3- vibrations. J Chem Phys 49:4600–4610CrossRefGoogle Scholar
  8. 8.
    Pezzotti G (2013) Raman spectroscopy of piezoelectrics. J Appl Phys 113:211301-1–78Google Scholar
  9. 9.
    Pezzotti G, Okai K, Zhu W (2012) Stress tensor dependence of the polarized Raman spectrum of tetragonal barium titanate. J Appl Phys 111:013504-1–16Google Scholar
  10. 10.
    Pezzotti G, Hagiwara H, Zhu W (2013) Quantitative investigation of Raman selection rules and validation of the secular equation for trigonal LiNbO3. J Phys D: Appl Phys 46:145103-1-13Google Scholar
  11. 11.
    Takahashi Y, Puppulin L, Zhu W, Pezzotti G (2010) Raman tensor analysis of ultra-high molecular weight polyethylene and its application to study retrieved hip joint components. Acta Biomater 6:3583–3594CrossRefGoogle Scholar
  12. 12.
    Tsuda H, Arends J (1994) Orientational micro-Raman spectroscopy on hydroxyapatite single crystals and human enamel crystallites. J Dent Res 73:1703–1710Google Scholar
  13. 13.
    Tsuda H, Arends J (1997) Raman spectroscopy in dental research: a short review of recent studies. Adv Dent Res 11:539–547CrossRefGoogle Scholar
  14. 14.
    Ko AC-T, Choo-Smith L-P, Hewko M, Leonardi L, Sowa MG, Dong CCS, Williams P, Cleghorn B (2005) Ex vivo detection and characterization of early dental caries by optical coherence tomography and Raman spectroscopy. J Biomed Opt 10:031118-1-16Google Scholar
  15. 15.
    Ko AC-T, Choo-Smith L-P, Hewko M, Sowa MG, Dong CCS, Cleghorn B (2006) Detection of early dental caries using polarized Raman spectroscopy. Opt Express 14:203–215CrossRefGoogle Scholar
  16. 16.
    Ko AC, Hewko M, Sowa MG, Dong CCS, Cleghorn B, Choo-Smith L-P (2008) Early dental caries detection using a fibre-optic coupled polarization-resolved Raman spectroscopic system. Opt Express 16:6274–6284CrossRefGoogle Scholar
  17. 17.
    Ionita I (2009) Diagnosis of tooth decay using polarized micro-Raman confocal spectroscopy. Romanian Rep Phys 61:567–574Google Scholar
  18. 18.
    Choo-Smith L-P, Dong CCS, Cleghorn B, Hewko M (2008) Shedding new light on early caries detection. J Can Dent Assoc 74:913–918Google Scholar
  19. 19.
    Choo-Smith L-P, Hewko M, Sowa M (2010) Towards early dental caries detection with OCT and polarized Raman spectroscopy. Opt Express 2:O43Google Scholar
  20. 20.
    Hill W, Petrou V (2000) Caries detection by diode laser Raman spectroscopy. Appl Spectrosc 54:795–99CrossRefGoogle Scholar
  21. 21.
    Prabhakar NK, Kiran KN, Kala M (2011) A review of modern non-invasive methods for caries diagnosis. Arch Oral Sci Res 1:168–177Google Scholar
  22. 22.
    Ten Cate AR (2008) Oral Histology: Development, Structure, and Function. Mosby Elsevier, St Louis, p 3Google Scholar
  23. 23.
    Companion paper to this articleGoogle Scholar
  24. 24.
    Grisafe DA, Hummel FA (1970) Pentavalent ion substitutions in the apatite structure, part B. Color. J Solid State Chem 2:167–175CrossRefGoogle Scholar
  25. 25.
    Gilinskaya LG, Mashkovtsev RI (1995) Blue and green centers in natural apatites by ESR and optical spectroscopy data. J Struct Chem 36:76–86CrossRefGoogle Scholar
  26. 26.
    Porto SPS, Krishnan RS (1967) Raman effect of corundum. J Phys Chem 47:1009–1012CrossRefGoogle Scholar
  27. 27.
    MATHEMATICA 7.0, Wolfram Research, Inc.: Champaign, IL, USAGoogle Scholar
  28. 28.
    Sanchez-Pastenes E, Reyes-Gasga J (2005) Determination of the point and space groups for hydroxyapatite by computer simulation of CBED electron diffraction patterns. Rev Mexic Fis 51:525–529Google Scholar
  29. 29.
    Corno M, Busco C, Civalleri B, Ugliengo P (2006) Periodic ab initio study of structural and vibrational features of hexagonal hydroxyapatite Ca10(PO4)6(OH)2. Phys Chem Chem Phys 8:2464–2472CrossRefGoogle Scholar
  30. 30.
    Loudon R (1964) The Raman effect in crystals. Adv Phys 13:423–482CrossRefGoogle Scholar
  31. 31.
    van Gurp M (1995) The use of rotation matrices in the mathematical description of molecular orientation in polymers. Colloid Polym Sci 273:607–625CrossRefGoogle Scholar
  32. 32.
    Wigner EP (1959) Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra. Academic Press, New YorkGoogle Scholar
  33. 33.
    Jaynes ET (1957) Information theory and statistical mechanics. Phys Rev 106:620–630CrossRefGoogle Scholar
  34. 34.
    Perez R, Banda S, Ounaies Z (2008) Determination of the orientation distribution function in aligned single wall nanotube polymer nanocomposites by polarized Raman spectroscopy. J Appl Phys 103:074302-1-9Google Scholar
  35. 35.
    Simmons LM, Al-Jawad M, Kilcoyne SH, Wood DJ (2011) Distribution of enamel crystallite orientation through an entire tooth crown studied using synchrotron X-ray diffraction. Eur J Oral Sci 119:19–24CrossRefGoogle Scholar
  36. 36.
    Mahoney P (2012) Incremental enamel development in modern human deciduous anterior teeth. Am J Phys Anthropol 147:637–651CrossRefGoogle Scholar
  37. 37.
    Fernandes CP, Chevitarese O (1991) The orientation and direction of rods in dental enamel. J Prosthet Dent 65:793–800CrossRefGoogle Scholar
  38. 38.
    Scott JH, Symons NBB (1982) Introduction to Dental Anatomy. Churchill Livingstone, EdinburghGoogle Scholar
  39. 39.
    Bechtle S, Habelitz S, Klocke A, Fett T, Schneider GA (2010) The fracture behavior of dental enamel. Biomaterial 31:375–384CrossRefGoogle Scholar
  40. 40.
    Johansen E (1965) Tooth enamel: its composition, properties, and fundamental structure. Wright and Sons, BristolGoogle Scholar
  41. 41.
    Wilson RM, Elliot JC, Dowker SEP (1999) Rietveld refinement of the crystallographic structure of human dental enamel apatites. Am Mineral 84:1406–1414Google Scholar
  42. 42.
    Al-Jawad M, Steuwer A, Kilcoyne SH, Shore RC, Cywinski R, Wood DJ (2007) 2D mapping of texture and lattice parameters of dental enamel. Biomaterial 28:2908–2914CrossRefGoogle Scholar
  43. 43.
    Nelson DGA, Williamson BE (1982) Low-temperature laser Raman spectroscopy of synthetic carbonated apatites and dental enamel. Aust J Chem 35:715–727CrossRefGoogle Scholar
  44. 44.
    Legeros RZ (1990) Chemical and crystallographic events in the caries process. J Dent Res 69:567–574Google Scholar
  45. 45.
    Apap M, Goldberg G (1985) A new microsample grinding technique for quantitative determination of calcium and phosphorus in dental enamel. J Dent Res 11:1293–1295CrossRefGoogle Scholar
  46. 46.
    Rey C, Collins B, Goehl T, Dickson RI, Glimcher MJ (1989) The carbonate environment in bone mineral: a resolution-enhanced Fourier transform infrared spectroscopy study. Calcif Tissue Int 45:157–164CrossRefGoogle Scholar
  47. 47.
    Sauer GR, Zunic WB, Durig JR, Wuthier RE (1994) Fourier transform Raman spectroscopy of synthetic and biological calcium phosphates. Calcif Tissue Int 54:414–420CrossRefGoogle Scholar
  48. 48.
    Rey C, Shimizu M, Collins B, Glimcher MJ (1990) Resolution-enhanced Fourier transform infrared spectroscopy study of the environment of phosphate ions in the early deposit of a solid phase of calcium-phosphate in bone and enamel, and their evolution with age: 1. Investigations in the v 4 PO4 domain. Calcif Tissue Int 46:384–394CrossRefGoogle Scholar
  49. 49.
    Rey C, Shimizu M, Collins B, Glimcher MJ (1991) Resolution-enhanced Fourier transform infrared spectroscopy study of the environment of phosphate ion in the early deposits of a solid phase of calcium phosphate in bone and enamel and their evolution with age: 2. Investigations in the v 3 PO4 domain. Calcif Tissue Int 49:383–388CrossRefGoogle Scholar
  50. 50.
    Trombe JC (1973) Contribution à l'étude de la décomposition et de la réactivité de certaines apatites hydroxylées et carbonates. Ann Chim Paris 8:251–269Google Scholar
  51. 51.
    De Mul FFM, Hottenhuis MHJ, Bouter P, Greve J, Arends J, Ten Bosch JJ (1986) Micro-Raman line broadening in synthetic carbonated hydroxyapatite. J Dent Res 65:437–440CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Giuseppe Pezzotti
    • 1
    • 2
    Email author
  • Wenliang Zhu
    • 3
  • Marco Boffelli
    • 1
  • Tetsuya Adachi
    • 4
  • Hiroaki Ichioka
    • 4
  • Toshiro Yamamoto
    • 4
  • Yoshinori Marunaka
    • 2
    • 5
  • Narisato Kanamura
    • 4
  1. 1.Ceramic Physics LaboratoryKyoto Institute of TechnologyKyotoJapan
  2. 2.Department of Molecular Cell Physiology, Graduate School of Medical ScienceKyoto Prefectural University of MedicineKyotoJapan
  3. 3.Department of Medical Engineering for Treatment of Bone and Joint DisordersOsaka UniversitySuitaJapan
  4. 4.Department of Dental Medicine, Graduate School of Medical ScienceKyoto Prefectural University of MedicineKyotoJapan
  5. 5.Department of Bio-Ionomics, Graduate School of Medical ScienceKyoto Prefectural University of MedicineKyotoJapan

Personalised recommendations