Abstract
Density functional theory-based calculations within the framework of the plane-wave pseudopotential approach are carried out to define the phonon spectrum of hydroxyapatite \(\mathrm{Ca}_{10}(\mathrm{PO}_{4})_{6}(\mathrm{OH})_{2}\) (HAp). It allows to describe the temperature dependence of the electronic spin-lattice relaxation time \(\mathrm{T}_{1e}\) of the radiation-induced stable radical \(\mathrm{NO}_{3}^{2-}\) in HAp, which was measured in X-band (9 GHz, magnetic field strength of 0.34 T) in the temperature range T = (10–300) K. It is shown that the temperature behavior of \(T_{1e}\) at \(T>\) 20 K can be fitted via two-phonon Raman type processes with the Debye temperature \(\Theta _{\mathrm{D}} \approx 280\,{\mathrm{K}}\) evaluated from the phonon spectrum.
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Acknowledgments
We dedicate this investigation to our teacher, colleague, and friend Dr. Igor N. Kurkin who has been actively engaged in EPR research at Kazan University since the beginning of 1960s and who is going to celebrate his 75th birthday in 2016 in front of an EPR spectrometer.This work was supported by the subsidy allocated to Kazan Federal University for the project part in the sphere of scientific activities. M.G. acknowledges the support of the Program of competitive Growth of Kazan Federal University among World’s Leading Academic Centers.
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Biktagirov, T., Gafurov, M., Iskhakova, K. et al. Phonon Spectrum in Hydroxyapatite: Calculations and EPR Study at Low Temperatures. J Low Temp Phys 185, 627–632 (2016). https://doi.org/10.1007/s10909-015-1419-2
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DOI: https://doi.org/10.1007/s10909-015-1419-2