## 2 Materials and Methods  
### Fabrication of Nano Coated CaF\({}_{2}\)@Al(OH)\({}_{3}\) Powder  
The preparation process of nano coated CaF\({}_{2}\)@Al(OH)\({}_{3}\) powder was as follows: The ethanol, benzene and water were mixed according to the volume ratio of 6:2:1 as a solvent. The polyvinylpyrrolidone (PVP) was added to prepare the solution containing 0.5 mol/L. The nano CaF\({}_{2}\) (5-10 nm, self-made) was added to prepare the solution containing CaF\({}_{2}\) 0.1 mol/L, and afterward ultrasonic treatment was carried out for 40 min. The dilute ammonia water was mixed alcohol and ammonia water with a volume ratio of 5:1. The CaF\({}_{2}\) suspension was stirred with a magnetic stirrer (DF-101S) at 25 \({}^{\circ}\)C. The aluminum nitrate solution of 0.5 mol/L was slowly poured into the CaF\({}_{2}\) suspension, and the solution was continuously stirred for 20 min until the solution was uniform. Dropwise, diluted ammonia water was added at 2 mL/min to adjust the pH of the solution to 7. The Al(OH)\({}_{3}\) finally formed the heterogeneous nucleation coating on the surface of nano CaF\({}_{2}\). The nano coated CaF\({}_{2}\)@Al\({}_{2}\)O\({}_{3}\) powder can be obtained by centrifuging, washing and sintering the CaF\({}_{2}\)@Al(OH)\({}_{3}\).  
Fabrication of Al\({}_{2}\)O\({}_{3}\)Ti(C,N)/ZrO\({}_{2}\)/CaF\({}_{2}\)@Al(OH)\({}_{3}\) Ceramic Material  
Commercially available Al\({}_{2}\)O\({}_{3}\) (200 nm, purity \(\geq\) 99.9%, Shanghai Chaowei New Material Co., Ltd., Shanghai, China) and Ti(C,N) (80 nm, purity \(\geq\) 99.9%, Hefei Yulong New Material Co., Ltd., Hefei, China) used here were raw materials. The ZrO\({}_{2}\) whisker (mean diameter and length were 1-3 \(\upmu\)m and 10-20 \(\upmu\)m, respectively) was raw material. MgO (1 \(\upmu\)m, purity \(\geq\) 99.9%, Sinopharm Chemical ReagentCo., Ltd., Shanghai, China) was used as a sintering aid. Polyethylene glycol (PEG 4000, Sinopharm Chemical Reagent Co., Ltd., Shanghai, China) was the dispersant.  
The Al\({}_{2}\)O\({}_{3}\) and MgO powders, Ti(C,N) powders were added to the absolute ethyl alcohol with polyethylene glycol, respectively. Then, the dispersions were ultrasonically dispersed and mechanically stirred for 20-30 min. Mixing the Al\({}_{2}\)O\({}_{3}\) dispersion, the Ti(C,N) dispersion and the dispersion containing the nano coated CaF\({}_{2}\)@Al(OH)\({}_{3}\) powder, the mixed solution was ultrasonically dispersed and mechanically stirred for 10-30 min, thereafter the dispersion was poured into ball mill tank for ball milling. After 44 h of ball milling, the ZrO\({}_{2}\) whisker was added to the ball mill tank. The prepared multiphase suspension was dried in the vacuum drying oven (DZF-6050, Shanghai, China), and then the multiphase suspension was sieved to obtain composite powder. The composite powder was put into a graphite sleeve for cold-pressing. After the hot pressing in the vacuum hot-pressing sinter (ZR1050, Jinan, China), the Al\({}_{2}\)O\({}_{3}\)/Ti(C,N)/ZrO\({}_{2}\)/CaF\({}_{2}\)@Al(OH)\({}_{3}\) ceramic material was fabricated. The preparation process influenced the microstructure and further influenced properties of the material [34; 35]. The parameters selected in this experiment were as follows: the sintering temperature was set to 1650 \({}^{\circ}\)C under 30 MPa, the soaking time was selected as 20 min and the heating rate of the preparation progress was set to 20 \({}^{\circ}\)C/min. Figure 1 shows the process flow chart of the composite ceramic material preparation.