## 2 Materials and Method
### Experiment  
The experiment was conducted following five steps: Activation, extraction of silicon and aluminum, synthesis of precipitated silica, synthesis of zeolites, and REEs leaching. Parallel experiments were conducted to ensure the reproducibility of the results. Figure 2 shows the experimental scheme, and the detailed procedures were given as follows:  
1. Sample activation: First, 1 g of the CFA sample was quantitatively weighed. The alkali additive of Na\({}_{2}\)CO\({}_{3}\) was weighed and mixed with the CFA sample at a molar ratio of 1:1 (the ratio of silicon and aluminum content to the additive). The mixtures were calculated in a muffle furnace to a certain temperature of 850 \({}^{\circ}\)C and maintained for a desirable time of 80 min. Then, the sample was cooled to an ambient temperature and ground in agate mortar for the subsequent procedures. 2. Leaching of silicon and aluminum: The activated sample was transferred to a beaker and stirred with 20 mL of deionized water at an ambient temperature for 30 min. The solid-liquid separation was performed and repeated three times. To maximize the silicon and aluminum recovery through alkali leaching of the activated CFA sample, the process was optimized for the process parameters, i.e., NaOH concentration, heating temperature, solid-liquid ratio, and holding time. The desired concentration of the NaOH solution and other factors was based on the orthogonal table (Table 2). The washed samples were transferred to a round-bottom flask, and the bottle mouth was tightened with a rubber plug. The round-bottom flask was placed in an oil bath at a set temperature by magnetic stirring. The sample was centrifuged to separate the solid-liquid phase after the reaction. Leaching solution after water and alkali washing and separation was subject to the determination of Si and Al using ICP-OES (Inductively Coupled Plasma Optical Emission Spectrometer) (ICAP 7400, Waltham, MA, USA). 3. Synthesis of precipitated silica: The water washing solution of the activated CFA sample was collected and transferred to a beaker. CO\({}_{2}\) gas was introduced at a controlled flow rate and the pH was monitored until the solution pH stabilized at about 8.00. The solution was then transferred to the centrifugal tube and aged for 24 h at an ambient temperature. Thereafter, the solid-phase sample was separated and washed with deionized water several times and finally dried at 100 \({}^{\circ}\)C to obtain the precipitated silica product. 4. Synthesis of zeolites: The solution obtained during the alkali leaching experiment was used as the mother liquor for the synthesis of zeolite via the hydrothermal crystallization method [35]. The solution was stored at an ambient temperature for 24 h, and the precipitation of an orange-yellow solid in the solution was observed. The solid-liquid mixtures were transferred to the crystallization kettle and crystallized at 100 \({}^{\circ}\)C for 1, 3 and 5 h, and then followed by the separation of the solid-phase sample and washed with deionized water several times. Finally, the solid sample was dried in the oven at 100 \({}^{\circ}\)C to obtain zeolite products, and the separated liquid-phase sample can be used as a fresh alkali washing solution for activated CFA samples. 5. Leaching of REEs: The solid sample residue after the aforementioned activation and washing procedure was respectively added into 20 mL of deionized water and stirred evenly in a constant ambient temperature using a magnetic stirrer. A certain volume of concentrated hydrochloric acid was gradually added with a pipette gun to maintain the solution pH at 2.00. Finally, the liquid-phase sample was separated and subject to the determination of REEs using ICP-MS (ICAP-Q, Waltham, MA, USA). For the characterization of value-added solid products, the crystalline phase evolution of zeolites was analyzed by XRD (SmartLab, Tokyo, Japan) with Cu K\(\alpha\) radiation (40 kV, 40 mA) at a scan rate of 2\({}^{\circ}\)/min and step size of 0.0167\({}^{\circ}\).