Introduction Fluorescent materials have attracted much attention due to their application advantages in solar cells, biological diagnostics, infrared detection and solid-state laser. Up-conversion luminescence process refers to a special anti-stokes process that converts low-energy photons into high-energy photons. Rare-earth element doped fluoride nanoparticles are beneficial to obtaining a high up-conversion luminescence efficiency due to their low phonon energy. However, the lack of particle morphology and stability of the nanoparticles hinders their practical application. From the perspective of application analysis, rare-earth element doped fluoride crystal materials have a lower cost and a better stability, and are more suitable for complex occasions where bulk materials are needed. Er3+ ion is widely used in various up-conversion optical materials because it can emit green or red fluorescence under the excitation at 980 or 808 nm laser. From the perspective of luminescence, rare-earth element ion has a poor luminescence performance in the crystal environment with a high symmetry due to the prohibition of electric dipole transition. For the luminescence of doped ions, substances with a low symmetry system should have more potential advantages. Strontium fluorophosphates (Sr5(PO4)3F (referred to as S-FAP) crystal material is considered as a member of the hexagonal crystalline system fluorapatite family. The synthesis of high-quality single crystal has challenges. The single crystal growth process has frequent performance defects such as bubbles, clouds, cracks and impurity absorption. In this paper, a high quality strontium fluorophosphate transparent ceramic material was synthesized via conventional one-step hot pressing sintering as an economic way. In addition, the up-conversion luminescence properties of Er3+ in hexagonal strontium fluorophosphate asymmetric transparent polycrystalline ceramic material were also investigated.Materials and method The phase composition of 2% Er:S-FAP powder and ceramics was analyzed by a model D/Max-RB X-ray diffractometer (XRD) with Cu target at a tube voltage of 60 kV, tube current of 50 mA, scanning angle range of 20°-80°, and scanning step of 0.02°. The Rietveld refinement results of XRD were completed by a software named FullProf. The microstructure of powder and ceramic was determined by a model SU8010 field emission scanning electron microscope (SEM). For the SEM determination, the powder and ceramic samples were treated with gold spraying for 15 s and 20 s, respectively. The grain sizes of powder and ceramic samples were analyzed via softwares named nano Measure 1.2 and Image J. The optical linear transmittance and absorption spectra of 2% Er:S-FAP transparent ceramics were measured by a model UV-3600 UV-Visible-infrared spectrophotometer. The emission spectrum and fluorescence lifetime of ceramic samples at room temperature were measured by a model FLS1000 fluorescence spectrometer with excitation laser at 980 nm. All the tests were conducted at room temperature. The diameter and thickness of the ceramic samples were 16 mm and 2.2 mm, respectively.Results and discussion Based on the XRD patterns of 2% Er:S-FAP precursor powder and the XRD Rietveld refinement results of hot-pressing ceramics, the synthesized phase crystal structure is a hexagonal fluorapatite crystal structure. The SEM results of the powder show that the short rod-like fluorapatite nanoparticles with a high sintering activity and a well dispersion can be synthesized by a simple liquid-phase co-precipitation method. The average grain size is (19.10±1.6) nm, which is similar to the calculated value (i.e., 17.0 nm). The existence of compact and uniform surface and sectional structure is a basis of high optical quality 2% Er:S-FAP transparent ceramics, and the average grain size of the ceramics is (386.6±20.8) nm. The linear optical transmittance of the ceramic samples at 500 nm and 1 000 nm is 66.14% and 84.41%, respectively. The linear optical transmittance of 2% Er:S-FAP transparent ceramics is not close to the theoretical transmittance possibly due to some factors that reduce the transmittance (i.e., impurity scattering, porosity, and grain boundary birefringence). The actual average grain size of transparent ceramics is less than 1 μm. The scattering caused by coarse grain boundaries is small, and the pore and grain boundary birefringent scattering is a main reason of light scattering loss. The intensity of all emission peaks of 2% Er:S-FAP polycrystalline transparent ceramics increases with the increase of laser power intensity, and the intensity of emission peaks related to red emission at 661 nm is more obvious. The up-conversion luminescence process of Er3+ in S-FAP ceramic matrix, including red and green light emission, is dominated by a two-photon absorption process through fitting of excitation power P and up-conversion emission intensity Iuc. 2% of Er3+ emits an intense red light in S-FAP matrix when exciting Er3+ by a laser at 980 nm after Er3+ occupies Sr2+ site. The enhanced cross relaxation effect between Er3+-Er3+ leads to the relative enhancement of red emission relative to green emission. The specific cross relaxation process is as follows: i.e., 1) 4F7/2 + 4I11/2→409/2 + 4F9/2; 2) 4S3/2 + 4I15/2→4I9/2 + 4I13/2; and 3) 4I13/2 + 4I11/2→4I15/2 + 4F9/2.Conclusions The XRD and SEM results show that 2% Er:S-FAP nano-powder with a short rod-like morphology and an average grain size of (19.10±1.6) nm was synthesized. The superior linear optical transmittance of the ceramic was due to the high dense and uniform ceramic cross section and surface microstructure. The optical transmittance of the ceramic at 500-1 000 nm was 66.14 and 84.41%, respectively. The scattering factor of the ceramic was mainly grain boundary birefringent scattering. The absorption spectra at room temperature show that the absorption peak intensity of green light of Er3+ in S-FAP transparent ceramic was greater than that of red light. The intensity of the red emission peak of the ceramic was greater than that of the green light in the up-conversion emission spectrum as the laser pump power at 980 nm increases possibly due to the enhancement of cross relaxation phenomenon. Two-photon absorption dominates the up-conversion process of 2% Er3+ in S-FAP transparent ceramic matrix by means of the intensity of red-green upconversion light with the excitation power of the laser. It is indicated that Er3+:S-FAP transparent ceramic material is a kind of red up-conversion luminescent material with a promising application potential.