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The q-deformed Fermi-Dirac distribution is used to study the high-temperature F ( ) T T ∨ behavior of a relativistic q-deformed ideal Fermi gas. The effects of the q-deformation and relativity on the properties of the system are discussed, and then, the example of the neutrinos near the surface of the earth is used to calculate approximately. It shows that the q-deformation increases the total energy but decreases the chemical potential and heat capacity, whereas 2 F0 mc ε increases the chemical potential and total energy but decreases the heat capacity ( F0 ε is the Fermi energy of ultrarelativistic undeformed Fermi gas). The larger the deformation parameter q and the value of 2 F0 mc ε are, the more remarkable the effects of them on the thermostatistic properties will be. However, the effects of both q-deformation and relativity become weak with increasing temperature. When the temperature , T → ∞ the thermostatistic properties of the system are reduced to those of ordinary Boltzmann gases and independent of q and relativity effect completely, which implies that the q-deformation is a pure quantum effect.

By employing a certain proportion of hydrogen peroxide, ammonia, ammonium fluoride, and ethylene diamine tetraacetic acid (EDTA) as precipitator, well-crystallized LaOF:Eu3+ and LaOF:Yb3+, Er3+ nanocrystals are synthesized by using the chemical co-precipitation method. The structural properties of these samples are characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), and Fourier transform infrared spectroscopy (FTIR) spectra. The results show that all the samples have an average size below 70 nm, which decreases gradually with the increase of the EDTA content, and a certain number of EDTA molecules are coupled with doped ions on the surfaces of nanocrystals. Most of the doped ions are proved to be enriched on the surfaces of nanocrystals and surrounded by the high energy vibration groups and bonds in EDTA molecules. The observed differences in upconversion emission spectrum among the different LaOF:Yb3+, Er3+ nanocrystals are explained by the different two-photon upconversion mechanisms. Especially, in the LaOF:Yb3+, Er3+ nanocrystals with EDTA, the two-photon processes that contain several special cross-relaxation processes are introduced to analyse the corresponding upconversion mechanisms.

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