Poisson’s ratio of fluorapatite crystals

DOI: https://doi.org/10.29296/24999490-2023-06-05

S.A. Muslov, R.Sh. Gvetadze, S.D. Arutyunov
Moscow State Medical and Dental University named after. A.I. Evdokimova,
st. Delegatskaya, 20, building 1, Moscow, 127473, Russian Federation

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.
Keywords: 
fluorapatite, Poisson’s ratio, biomechanics and bioengineering
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