Poisson’s ratio of fluorapatite crystals
- Authors: Muslov S.A.1, Gvetadze R.S.1, Arutyunov S.D.1
-
Affiliations:
- Moscow State Medical and Dental University named after. A.I. Evdokimova
- Issue: Vol 21, No 6 (2023)
- Pages: 33-40
- Section: Reviews
- URL: https://journals.eco-vector.com/1728-2918/article/view/624953
- DOI: https://doi.org/10.29296/24999490-2023-06-05
- ID: 624953
Cite item
Abstract
Introduction. It is known that in the pathogenesis of caries and non-carious lesions of teeth, an important role is played by enamel resistance, which is determined by numerous factors, among which the structure and physical and mechanical properties of tooth tissues are considered to be among the most important. This report summarizes the literature data on the Poisson’s ratio of fluorapatite (FAp), a biomaterial and one of the mineral components of dental hard tissues. The literature search was carried out in electronic databases Scopus, Web of Science, PubMed, Medline, Elibrary, MatWeb for the period from January 1970 to March 2023 inclusive. Some of the data are supplemented by our own calculations based on formulas for crystalline hexagonal systems (systems). As is known, Poisson’s ratio determines the volumetric response of materials and biological tissues to mechanical load, but its anisotropic properties have not been studied in detail.
Material and methods. Calculations of the Poisson’s ratio of fluorapatite were carried out in the computer algebra system Mathcad 15.0, using the online analysis of elasticity tensors ELATE, and an integrated molecular modeling system was used - the graphic package VESTA (Visualization for Electronic and STructural Analisis).
Results and discussion. The Poisson’s ratio values of fluorapatite crystals varied: minimum values 0.057–0.283, maximum values 0.302–0.494, average values obtained by integration in all directions 0.24–0.308. The coefficient of elastic anisotropy of the fluorapatite crystal lattice, calculated based on the values of Poisson’s ratio, is 1.21–5.29. The results obtained were compared with those of hydroxyapatite (HAp) crystals, dentin, enamel and filling materials. The highest values of the parameters μ and μmax are found in dentin (0.312 and 0.54), the lowest μmin are also found in dentin (0.13).
Conclusions. Fluorapatite crystals are elastically anisotropic, and Poisson’s ratio μmax/μmin varies over a wide range. The Poisson’s ratio of fluorapatite showed similarity with the transverse strain coefficient of isomorphic hydroxyapatite crystals (0.207–0.374), dentin (0.13–0.54), enamel (0.16–0.47) and dental composite filling materials (0.24–0 ,35). The latter should help improve the quality of restorations using filling materials for replacing hard dental tissues. It has been established that the organic component of dentin increases its Poisson’s ratio as a biocomposite and the anisotropy of elastic properties.
Full Text
![Restricted Access](https://journals.eco-vector.com/lib/pkp/templates/images/icons/text_lock.png)
About the authors
Sergey A. Muslov
Moscow State Medical and Dental University named after. A.I. Evdokimova
Author for correspondence.
Email: muslov@mail.ru
ORCID iD: 0000-0002-9752-6804
Professor of Department of normal physiology and medical physics, Doctor of biological sciences, candidate of physics and mathematical sciences, Associated professor
Russian Federation, st. Delegatskaya, 20, bl. 1, Moscow, 127473Ramaz S. Gvetadze
Moscow State Medical and Dental University named after. A.I. Evdokimova
Email: ramaz-gvetadze@yandex.ru
ORCID iD: 0000-0003-0508-7072
professor of the Department of Digital Dentistry, Doctor of medical sciences, professor, Corresponding Member RAS
Russian Federation, st. Delegatskaya, 20, bl. 1, Moscow, 127473Sergey D. Arutyunov
Moscow State Medical and Dental University named after. A.I. Evdokimova
Email: sd.arutyunov@mail.ru
ORCID iD: 0000-0001-6512-8724
Head of Department of Digital Dentistry, Doctor of medical sciences, professor, Honored Doctor of the Russian Federation, Honored Worker of Science of the Russian Federation
Russian Federation, st. Delegatskaya, 20, bl. 1, Moscow, 127473References
- Русских И.С. Роль фторидов в профилактике кариеса зубов. Актуальные исследования, 2020; 23 (26): 55–7. [Russkikh I.S. The role of fluorides in the prevention of dental caries. Actual research [Aktual’nye issledovanija]. 2020; 23 (26): 55–7 (in Russian)]
- Кузьмина Э.М., Янушевич О.О. Профилактическая стоматология. IBSN: 978-5-98811-385-0, М.: Практическая медицина, 2017; 262. [Kuzmina E.M., Yanushevich O.O. Preventive dentistry. M.: Prakticheskaya meditsina, 2017; 262 (in Russian).]
- Лебеденко И.Ю., Арутюнов С.Д., Муслов С.А., Усеинов А.С. Нанотвердость и модуль Юнга зубной эмали. Вестник Российского университета дружбы народов. Серия: Медицина, 2009; 4: 637–8. [Lebedenko I.Yu., Arutyunov S.D., Muslov S.A., Useinov A.S. Nanohardness and Young’s modulus of tooth enamel. Bulletin of RUDN. Series: Medicine, 2009; 4: 637–8 (in Russian)]
- Qanbar A., Abdulla A.A.M., Abutayyem H. and El Din Mohamed S.K. Comparative evaluation of the efficacy of silver diamine fluoride, sodium fluoride and GC tooth mousse plus and fluoride varnish as an antibacterial agent in childhood caries: As a literature review. Dental. Res. Manag. 2001; 5: 1–7. DOI: 10,33805/2572-6978.150
- Katz J.L., Ukraincik K.J. On the anisotropic elastic properties of hydroxyapatite. Biomech. 1971; 4 (3): 221–7. DOI: 10,1016/0021-9290(71)90007-8.
- Муслов С.А., Арутюнов С.Д. Механические свойства зуба и околозубных тканей. Монография. IBSN: 978-5-98811-617-2. М.: Практическая медицина, 2020; 256. [Muslov S.A., Arutyunov S.D. Mechanical properties of the tooth and peridental tissues. Monograph. M.: Prakticheskaya meditsina, 2020; 256 (in Russian)]
- Muslov S.A., Lisovenko D.S., Arutyunov А.S., Pivovarov A.A., Manin A.I., Kirakosyan L.G., Kharah Y.N., Arutyunov S.D. The Poisson’s ratio of dentin as anisotropic medium with hexagonal symmetry. Russian Journal of Biomechanics, 2018; 22 (4): 472–9. DOI: 10,15593/RJBiomech/2018.4.09.
- Menendez-Proupin S. Cervantes-Rodrıguez R., Osorio-Pulgar M., Franco-Cisterna H. Camacho-Montes and M.E. Fuentes J. Mech. Behav. Biomed. Mater. 2011; 4: 1011–20, DOI: 10,1016/j.jmbbm.2011.03.001.
- Mostafa N.Y., Brown P.W. Computer simulation of stoichiometric hydroxyapatite: structure and substitutions. J. Phys. Chem. Solids, 2007; 68: 431–7. https://doi.org/10,1016/j.jpcs.2006.12.011.
- De Leeuw N.H., Bowe J.R., Rabone J. A computational investigation of stoichiometric and calcium-deficient oxy- and hydroxyapatites. Faraday Discuss. 2007; 134: 195–214. https://doi.org/10,1039/B602012G.
- Yoon H.S., Newnham R.E. Elastic properties of fluorapatite. Am. Mineral. 1969; 54: 1193–7.
- Gilmore R.S., Katz J.L. Elastic properties of apatites. J. Mater. Sci., 1982; 17: 1131–41. https://doi.org/10,1007/BF00543533.
- Sha M., Li Z., Bradt R.C. Single-crystal elastic constants of fluorapatite Ca5F(PO4)3. J. Appl. Phys., 1994; 75: 7784–7.
- Biskri Z.E., Rached H., Bouchear M., Rached D. and Aida M.S. A Comparative Study of Structural Stability and Mechanical and Optical Properties of Fluorapatite (Ca5(PO4)3F) and Lithium Disilicate (Li2Si2O5) Components Forming Dental Glass–Ceramics: First Principles Study. J. of Electronic Materials. 2016; 45: 5082–95. DOI: 10,1007/s11664-016-4681-4.
- Li C.X., Duan Y.H. and Hu W.C. Electronic Structure, Elastic Anisotropy, Thermal Conductivity and Optical Properties of Calcium Apatite Ca5(PO4)3X (X = F, Cl or Br). J. of Alloys and Compounds. 2015; 619: 66–77. https://doi.org/10,1016/j.jallcom.2014.09.022N.
- Ereifej F.P., Rodrigues N., Silikas and D.C. Watts. Experimental and FE shear-bonding strength at core/veneer interfaces in bilayered ceramics Dent. Mater. 2011; 27: 590, DOI: 10,1016/j.dental.2011.03.001.
- Studart A.R., Filser F., Kocher P., Heinz Luthy H., and Gauckler L.J. Mechanical and fracture behavior of veneer–framework composites for all-ceramic dental bridges. Dent. Mater. 2007; 23: 115. DOI: 10,1016/j.dental.2005.12.009.
- ELATE
- Elastic tensor analysis. Интернет-ресурс. URL: https://progs.coudert.name/elate. Дата доступа: 10,08.23.
- Thompson R.P., Clegg W.J. Predicting whether a material is ductile or brittle. Current Opinion in Solid State & Materials Science. 2018; 100–8. https://doi.org/10,1016/j.cossms.2018.04.001.
- Муслов С.А., Зайцева Н.В., Чистяков М.В. Коэффициент Пуассона гидроксиапатита в кристаллическом и поликристаллическом состоянии. VIII Международная научно-практическая конференция “Актуальные аспекты развития науки и общества в эпоху цифровой трансформации”. 2023; 257–67. [Muslov S.A., Zaitseva N.V., Chistyakov M.V. Poisson’s ratio of hydroxyapatite in the crystalline and polycrystalline state. VIII International Scientific and Practical Conference “Actual aspects of the development of science and society in the era of digital transformation”. 2023; 257–67 (in Russian)]
- Sew Meng Chung, Adrian U Jin Yap, Wee Kiat Koh, Kuo Tsing Tsai, Chwee Teck Lim. Measurement of Poisson’s ratio of dental composite restorative materials. Biomaterials. 2004; 25: 2455–60, DOI: 10,1016/j.biomaterials.2003.09.029.
- Nassar Y., Brizuela M. The Role of Fluoride on Caries Prevention. [Updated 2023 Mar 19]. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2023 Jan-Available from: https://www.ncbi.nlm.nih.gov/books/NBK587342/.
Supplementary files
![](/img/style/loading.gif)