# Thermometric Characterization of Fluorescent Nanodiamonds Suitable for Biomedical Applications
## 3 Results and Discussion
### Nanothermic Scale of High-Pressure High-Temperature Nanodiamonds  
The fluorescence spectrum of 35 nm, 70 nm and 100 nm-sized nanodiamonds are shown in Figure 1b. The two fluorescence peaks detected at 575 nm and 637 nm correspond to the NV\({}^{0}\) and NV\({}^{-}\) colour centres defects' fluorescence, respectively. An energy level diagram for both charge states is shown in Figure 1a, illustrating which energy levels are found in either charge state configuration symmetry. The NV\({}^{0}\) zero-phonon line transition \({}^{2}\)A\({}_{2}\)-\({}^{2}\)E has an energy of 2.15 eV corresponding to 575 nm. The NV\({}^{-}\) zero-phonon line transition \({}^{3}\)E-\({}^{3}\)A\({}_{2}\) has an energy of 1.94 eV corresponding to 637 nm. The two peaks detected at 659 nm and 680 nm are NV\({}^{-}\) phonon sidebands ascribed to an electron-phonon coupling [63; 64]. Optical excitation and emission are separated into zero-phonon lines and phonon sidebands. Vibrational properties determine the shape and extent of the phonon sidebands. In a radiative transition, the initial state is a vibrational ground state of an excited energy level, while the final state can be any vibrational state of the electronic ground state; hence, the phonon sideband transitions are usually Stokes-shifted [59; 64; 65]. The radiative transition \({}^{1}\)A\({}_{1}\)-\({}^{1}\)E of energy 1.19 eV corresponds to an infrared photon of a wavelength of 1042 nm and lies within the NV\({}^{-}\) electronic structure. Our results demonstrated how the NV centres' fluorescence from nanodiamonds is sensitive to temperature changes and can be accurately described by a linear model within the 25 \({}^{\circ}\)C to 60 \({}^{\circ}\)C range. Figure 2 shows how both charge states' fluorescence transforms concerning to temperature changes and their nanothermic scales adjusted employing a linear fit. Figure 1: **(a)** Energy level diagram of the NV\({}^{0}\) and NV\({}^{-}\) centres in the diamond crystal lattice. The solid arrows denote the energy separation from the energy level to the valence or conduction band, and E\({}_{\text{g}}\) is the diamond’s bandgap. The dashed arrows characterize the intersystem crossing between two energy levels. The wavy coloured arrows are the observed radiative transitions. **(b)** Fluorescence spectra of HPHT nanodiamonds of different sizes recorded at 25 \({}^{\circ}\)C. The top-coloured lines are normalized fluorescence spectra, the top dashed black lines are the baselines, the bottom-coloured lines are the filtered spectra, the bottom solid black lines are the Gaussian fits, and the bottom-coloured areas correspond to fluorescence peaks of the NV centres. The 35 nm nanodiamonds yielded a very accurate linear data representation and sensitivities of 97%, 5.37% \({}^{\circ}\)C\({}^{-1}\) (NV\({}^{0}\)) and 90%, 5.618\(\permperm\)\({}^{\circ}\) C\({}^{-1}\) (NV\({}^{-}\)), demonstrating outstanding thermometric performance. The 70 nm nanodiamonds yielded linear data representations of 82%, 6.365% \({}^{\circ}\)C\({}^{-1}\) (NV\({}^{0}\)) and 93%, 6.475% \({}^{\circ}\)C\({}^{-1}\) (NV\({}^{-}\)), performing slightly worse than the 35 nm-sized ones. The 100 nm nanodiamonds performed best among all the samples. They exhibited superior linear data representations of 98%, 6.994% \({}^{\circ}\)C\({}^{-1}\) (NV\({}^{0}\)) and 98%, 4.14% \({}^{\circ}\)C\({}^{-1}\) (NV\({}^{-}\)) than the other samples, mainly attributed to their high nitrogen-vacancy centre concentration [66; 67; 68] and their enhanced fluorescence signal of the NV\({}^{-}\) dominant charge state [23]. Remarkably, the reported sensitivities represent uncertainties around \(\pm\) 1.3 \({}^{\circ}\)C for both NV centres marginally bigger than those reported in ODMR experiments (\(\approx\)0.5-1 \({}^{\circ}\)C) [69; 70]. We observed how the 70 nm-sized nanodiamonds' NV\({}^{0}\) intensity exhibited an anomalous feature in the analysis, where a linear curve could only represent 82% of the data, whereas the 35 nm (93%) and 100 nm (98%) sized ones reached higher R\({}^{2}\) values.