A high-temperature, high-pressure synthesis method for yttrium silicate apatite (Ca 5-x Y x )[(PO4) 3-x (SiO3) 2x F's method

Abstract

This invention discloses a high-temperature, high-pressure synthesis method for yttrium silicate apatite (Ca). 5‑x Y x )[(PO4) 3‑x (SiO3) 2x The method described is as follows: Analytical grade calcium carbonate and analytical grade nano-silica were mixed in a 1:1 molar ratio and sintered at high temperature to obtain the precursor calcium silicate CaSiO3. Analytical grade calcium phosphate Ca3(PO4)2 and analytical grade nano-calcium fluoride CaF2 were mixed in a 3:1 molar ratio, ground uniformly, and then subjected to high temperature to obtain the precursor undoped apatite Ca5(PO4)3F powder. Calcium silicate, undoped apatite, analytical grade yttrium phosphate YPO4, and nano-calcium fluoride were mixed according to the reaction equation in molar ratio, where x is the doping amount of rare earth yttrium Y. The mixture was ground uniformly and reacted under high temperature and pressure to obtain yttrium silicate apatite powder. The obtained yttrium silicate apatite sample was a white powder, and the yttrium doping amount x ranged from 0.

Description

Technical Field

[0001] This invention relates to the field of earth science and mineralogy research, and specifically to a high-temperature, high-pressure synthesis method for yttrium silicate apatite (Ca). 5-x Y x )[(PO4) 3-x (SiO3) 2x The method of F. Background Technology

[0002] Rare earth apatite is a common mineral in igneous and metamorphic rocks, and an important carrier of rare earth elements, serving as a crucial mineral raw material for rare earth extraction. Its natural formation mechanism involves the formation of a complex rare earth silicate phosphate complex from monazite (YPO4) and silicates under high temperature and pressure in a water environment, namely yttrium silicate apatite (Ca). 5-x Y x )[(PO4) 3-x (SiO3) 2x Due to the significant differences in crystal forms between silicates and phosphates, the silicate-apatite composite crystal form cannot form a continuous solid solution and thus has a limiting solid solubility. Therefore, the Y content (x) of silicate-apatite has an upper limit, which is crucial for predicting the rare earth content in apatite deposits. Currently, most studies on the properties of yttrium-bearing silicate-apatite use natural minerals, while the quantification of the upper limit of solid solubility in artificial synthesis remains a gap. Summary of the Invention

[0003] The technical problem to be solved by this invention is: to provide a high-temperature and high-pressure synthetic method for yttrium silicate apatite (Ca). 5-x Y x )[(PO4) 3-x (SiO3) 2x The method of F was used to determine the doping range of rare earth Y in apatite.

[0004] The technical solution of this invention is: a high-temperature and high-pressure synthesis method for yttrium silicate apatite (Ca). 5-x Y x )[(PO4) 3-x (SiO3) 2x The method of F includes the following steps:

[0005] Step 1: Analytical grade calcium carbonate (CaCO3) and analytical grade nano-silica (SiO2) are mixed and ground evenly in a molar ratio of 1:1. Using a powder press, the mixture powder is placed in a Φ10 mold and pressed into a cylindrical shape of Φ10mm×10mm. The cylindrical shape is then placed on a ceramic boat lined with platinum sheets and sintered in a silicon molybdenum rod furnace at 1000℃ for 12 hours. After natural cooling, it is ground, pressed, and sintered again at 1200℃ for 12 hours. The precursor calcium silicate (CaSiO3) powder is obtained by grinding. The synthesis reaction is: CaCO3 + SiO2 → CaSiO3 + CO2.

[0006] Step 2: Analytical grade calcium phosphate Ca3(PO4)2 and analytical grade nano-calcium fluoride CaF2 are mixed and ground evenly at a molar ratio of 3:1. Using a powder press, the mixture powder is placed in a Φ10mm mold and pressed into a Φ10mm×10mm cylindrical shape. The cylindrical shape is placed on a ceramic boat lined with platinum sheets and sintered in a silicon molybdenum rod furnace at 1000℃ for 24 hours. The precursor undoped apatite Ca5(PO4)3F powder is obtained by grinding. The synthesis reaction is: 3Ca3(PO4)2 + CaF2 → 2Ca5(PO4)3F.

[0007] Step 3: The precursor phase calcium silicate (CaSiO3) synthesized in Steps 1 and 2, undoped apatite (Ca5(PO4)3F), analytical grade yttrium phosphate (YPO4), and analytical grade nano-calcium fluoride (CaF2) are mixed in molar proportions according to the left side of the reaction equation to obtain a mixture: (2-4x / 3)Ca5(PO4)3F + 2xYPO4 + 4xCaSiO3 + (2x / 3)CaF2 → 2(Ca 5-x Y x )[(PO4) 3-x (SiO3) 2x ]F, where x is the doping amount of rare earth yttrium Y. The mixture is ground evenly and then pressed into a Φ6mm×5mm cylinder using a powder presser. The cylinder is wrapped with a 0.02mm thick platinum foil and placed in an h-BN tube, with h-BN as the pressure transmission medium.

[0008] Step 4: Assemble the h-BN tube containing the sample from Step 3 into the high-pressure synthesis assembly block and place it in a six-sided top press for high-temperature and high-pressure reaction.

[0009] Step 5: After the high-temperature and high-pressure reaction is completed, the cylindrical tube wrapped in platinum foil is removed. A diamond cutter is used to cut the platinum tube, and the sample is extracted and ground to obtain yttrium silicate apatite powder (Ca). 5-x Y x )[(PO4) 3-x (SiO3) 2x ]F.

[0010] Further, the specific operation of the h-BN tube in step 3 is as follows: Drill a hole with a diameter of Φ6 mm in the center of an h-BN rod with a size of Φ10 mm on a lathe to make an h-BN tube, insert the sample into the tube, and seal both ends with h-BN sheets with a thickness of 2 mm and a diameter of Φ6 mm.

[0011] Further, the method of assembling the h-BN tube in the high-pressure synthesis assembly block described in step 4 specifically includes the following operations: Select a pyrophyllite block, drill a circular through-hole with a diameter of Φ12 mm in the center of the pyrophyllite block; sleeve a circular graphite heating furnace with an outer diameter of 12 mm and an inner diameter of Φ10 mm in the circular through-hole; place the sample sealed in a 10-mm h-BN tube in the middle of the graphite heating furnace; seal the upper and lower ends of the circular graphite heating furnace with pyrophyllite plugs.

[0012] Further, the high-temperature and high-pressure reaction conditions described in step 4 are as follows: First, increase the pressure to 1-3 GPa, then raise the temperature to 1050-1200 °C, hold the pressure and temperature for 2 h, and then quench.

[0013] Further, the obtained yttrium-containing silicate apatite sample described in step 5 is a white powder without other impurities, and its crystal structure is monoclinic P63 / m, and the lattice parameters α = 90°, β = 90°, γ = 120°. As the doping amount x of yttrium increases, the lattice parameters increase linearly.

[0014] Further, the range of the doping amount x of yttrium in the obtained yttrium-containing silicate apatite sample described in step 5 is 0 < x ≤ 0.15; when x > 0.15, a yttrium phosphate YPO4 impurity phase appears in the synthesis product.

[0015] Beneficial effects: The present application provides a method for artificially synthesizing yttrium-containing silicate apatite (Ca 5-x Y x )[(PO4) 3-x (SiO3) 2x F, which fills the blank of the existing technology without yttrium-containing silicate apatite and finds the solid solubility limit of artificially synthesizing yttrium-containing silicate apatite. Specific embodiments

[0016] Example 1:

[0017] A method for synthesizing yttrium-containing silicate apatite (Ca 4.95 Y 0.05 )[(PO4) 2.95 (SiO3) 0.10 F by high temperature and high pressure includes the following steps:

[0018] Step 1: Analytical grade calcium carbonate (CaCO3) and analytical grade nano-silica (SiO2) are mixed and ground uniformly at a molar ratio of 1:1. Using a powder press, the mixture is placed in a Φ10 mold and pressed into cylindrical pieces of Φ10mm × 10mm. These cylindrical pieces are then placed on a ceramic boat lined with platinum sheets and sintered in a silicon molybdenum rod furnace at 1000℃ for 12 hours. After natural cooling, the mixture is ground, pressed again, and sintered once more at 1200℃ for 12 hours. The resulting powder is the precursor calcium silicate (CaSiO3) powder. The synthesis reaction is: CaCO3 + SiO2 → CaSiO3 + CO2.

[0019] Step 2: Analytical grade calcium phosphate Ca3(PO4)2 and analytical grade nano-calcium fluoride CaF2 are mixed and ground evenly at a molar ratio of 3:1. Using a powder press, the mixture powder is placed in a Φ10mm mold and pressed into a Φ10mm×10mm cylindrical shape. The cylindrical shape is placed on a ceramic boat lined with platinum sheets and sintered in a silicon molybdenum rod furnace at 1000℃ for 24 hours. The precursor undoped apatite Ca5(PO4)3F powder is obtained by grinding. The synthesis reaction is: 3Ca3(PO4)2 + CaF2 → 2Ca5(PO4)3F.

[0020] Step 3: Mix the precursor phase calcium silicate (CaSiO3) synthesized in Steps 1 and 2, undoped apatite (Ca5(PO4)3F), analytical grade yttrium phosphate (YPO4), and analytical grade nano-calcium fluoride (CaF2) according to the molar ratio of the reaction equation: 29 / 15Ca5(PO4)3F + 1 / 10YPO4 + 1 / 5CaSiO3 + 1 / 30CaF2 → 2(Ca 4.95 Y 0.05 )[(PO4) 2.95 (SiO3) 0.10 F, where the doping amount of rare earth yttrium Y is x = 0.05. The mixture is ground uniformly, and the powder is pressed into a Φ6mm × 5mm cylinder using a powder press. The cylinder is then wrapped with a 0.02mm thick platinum foil. The platinum foil-wrapped sample cylinder is placed in an h-BN tube, with h-BN as the pressure transmission medium.

[0021] Step 4: Assemble the h-BN tube containing the sample from Step 3 into the high-pressure synthesis assembly block and place it in a six-sided top press for high-temperature and high-pressure reaction.

[0022] Step 5: After the high-temperature and high-pressure reaction is completed, the cylindrical tube wrapped in platinum foil is removed. A diamond cutter is used to cut the platinum tube, and the sample is extracted and ground to obtain silicate apatite powder with a yttrium content of x = 0.05 (Ca). 4.95 Y 0.05 )[(PO4) 2.95 (SiO3) 0.10 ]F.

[0023] The specific operation of the h-BN tube in step 3 is as follows: drill a 6mm hole in the center of an h-BN rod with a size of 10mm on a lathe to make an h-BN tube, insert the sample into the tube, and seal both ends with 6mm thick h-BN sheets.

[0024] The method for assembling the h-BN tube in the high-pressure synthesis assembly block as described in step 4 includes the following steps: selecting a pyrophyllite block and drilling a Φ12mm circular through hole in the center of the pyrophyllite block; fitting a circular graphite heating furnace with an outer diameter of 12mm and an inner diameter of Φ10mm inside the circular through hole; placing a 10mm h-BN tube-sealed sample in the middle of the graphite heating furnace; and sealing the upper and lower ends of the circular graphite heating furnace with pyrophyllite plugs.

[0025] The high-temperature and high-pressure reaction conditions described in step 4 are as follows: first, the pressure is increased to 1 GPa, then the temperature is increased to 1050℃, and the pressure and temperature are maintained for 2 hours before quenching.

[0026] Example 2:

[0027] A high-temperature, high-pressure synthesis method for yttrium silicate apatite (Ca 4.90 Y 0.10 )[(PO4) 2.90 (SiO3) 0.20 The method of F includes the following steps:

[0028] Step 1: Analytical grade calcium carbonate (CaCO3) and analytical grade nano-silica (SiO2) are mixed and ground uniformly at a molar ratio of 1:1. Using a powder press, the mixture is placed in a Φ10 mold and pressed into cylindrical pieces of Φ10mm × 10mm. These cylindrical pieces are then placed on a ceramic boat lined with platinum sheets and sintered in a silicon molybdenum rod furnace at 1000℃ for 12 hours. After natural cooling, the mixture is ground, pressed again, and sintered once more at 1200℃ for 12 hours. The resulting powder is the precursor calcium silicate (CaSiO3) powder. The synthesis reaction is: CaCO3 + SiO2 → CaSiO3 + CO2.

[0029] Step 2: Analytical grade calcium phosphate Ca3(PO4)2 and analytical grade nano-calcium fluoride CaF2 are mixed and ground evenly at a molar ratio of 3:1. Using a powder press, the mixture powder is placed in a Φ10mm mold and pressed into a Φ10mm×10mm cylindrical shape. The cylindrical shape is placed on a ceramic boat lined with platinum sheets and sintered in a silicon molybdenum rod furnace at 1000℃ for 24 hours. The precursor undoped apatite Ca5(PO4)3F powder is obtained by grinding. The synthesis reaction is: 3Ca3(PO4)2 + CaF2 → 2Ca5(PO4)3F.

[0030] Step 3: The precursor phase calcium silicate (CaSiO3) synthesized in Steps 1 and 2, undoped apatite (Ca5(PO4)3F), analytical grade yttrium phosphate (YPO4), and analytical grade nano-calcium fluoride (CaF2) are mixed according to the following molar ratio: 28 / 15Ca5(PO4)3F + 1 / 5YPO4 + 2 / 5CaSiO3 + 1 / 15CaF2 → 2(Ca 4.90 Y 0.10 )[(PO4) 2.90 (SiO3) 0.20 F, where the doping amount of rare earth yttrium Y is x = 0.10. The mixture is ground uniformly, and using a powder press, the powder is placed in a Φ6mm mold and pressed into a Φ6mm × 5mm cylindrical shape, which is then wrapped with a 0.02mm thick platinum foil. The platinum foil-wrapped cylindrical sample is placed in an h-BN tube, using h-BN as the pressure transmission medium;

[0031] Step 4: Assemble the h-BN tube containing the sample from Step 3 into the high-pressure synthesis assembly block and place it in a six-sided top press for high-temperature and high-pressure reaction.

[0032] Step 5: After the high-temperature and high-pressure reaction is completed, the cylindrical tube wrapped in platinum foil is removed. A diamond cutter is used to cut the platinum tube, and the sample is extracted and ground to obtain yttrium content x = 0.10 silicate apatite powder (Ca). 4.90 Y 0.10 )[(PO4) 2.90 (SiO3) 0.20 ]F.

[0033] The specific operation of the h-BN tube in step 3 is as follows: drill a 6mm hole in the center of an h-BN rod with a size of 10mm on a lathe to make an h-BN tube, insert the sample into the tube, and seal both ends with 6mm thick h-BN sheets.

[0034] The method for assembling the h-BN tube in the high-pressure synthesis assembly block as described in step 4 includes the following steps: selecting a pyrophyllite block and drilling a Φ12mm circular through hole in the center of the pyrophyllite block; fitting a circular graphite heating furnace with an outer diameter of 12mm and an inner diameter of Φ10mm inside the circular through hole; placing a 10mm h-BN tube-sealed sample in the middle of the graphite heating furnace; and sealing the upper and lower ends of the circular graphite heating furnace with pyrophyllite plugs.

[0035] The high-temperature and high-pressure reaction conditions described in step 4 are as follows: first, the pressure is increased to 2 GPa, then the temperature is increased to 1100℃, and the pressure and temperature are maintained for 2 hours before quenching.

[0036] Example 3:

[0037] A high-temperature, high-pressure synthesis method for yttrium silicate apatite (Ca 4.85 Y0.15 )[(PO4) 2.85 (SiO3) 0.30 The method of F includes the following steps:

[0038] Step 1: Analytical grade calcium carbonate (CaCO3) and analytical grade nano-silica (SiO2) are mixed and ground uniformly at a molar ratio of 1:1. Using a powder press, the mixture is placed in a Φ10 mold and pressed into cylindrical pieces of Φ10mm × 10mm. These cylindrical pieces are then placed on a ceramic boat lined with platinum sheets and sintered in a silicon molybdenum rod furnace at 1000℃ for 12 hours. After natural cooling, the mixture is ground, pressed again, and sintered once more at 1200℃ for 12 hours. The resulting powder is the precursor calcium silicate (CaSiO3) powder. The synthesis reaction is: CaCO3 + SiO2 → CaSiO3 + CO2.

[0039] Step 2: Analytical grade calcium phosphate Ca3(PO4)2 and analytical grade nano-calcium fluoride CaF2 are mixed and ground evenly at a molar ratio of 3:1. Using a powder press, the mixture powder is placed in a Φ10mm mold and pressed into a Φ10mm×10mm cylindrical shape. The cylindrical shape is placed on a ceramic boat lined with platinum sheets and sintered in a silicon molybdenum rod furnace at 1000℃ for 24 hours. The precursor undoped apatite Ca5(PO4)3F powder is obtained by grinding. The synthesis reaction is: 3Ca3(PO4)2 + CaF2 → 2Ca5(PO4)3F.

[0040] Step 3: The precursor phase calcium silicate (CaSiO3) synthesized in Steps 1 and 2, undoped apatite (Ca5(PO4)3F), analytical grade yttrium phosphate (YPO4), and analytical grade nano-calcium fluoride (CaF2) are mixed according to the following molar ratio: 9 / 5 Ca5(PO4)3F + 3 / 10 YPO4 + 3 / 5 CaSiO3 + 1 / 10 CaF2 → 2(Ca 4.85 Y 0.15 )[(PO4) 2.85 (SiO3) 0.30 F, where the doping amount of rare earth yttrium Y is x = 0.15. The mixture is ground uniformly, and using a powder press, the powder is placed in a Φ6mm mold and pressed into a Φ6mm × 5mm cylindrical shape, which is then wrapped with a 0.02mm thick platinum foil. The platinum foil-wrapped cylindrical sample is placed in an h-BN tube, using h-BN as the pressure transmission medium;

[0041] Step 4: Assemble the h-BN tube containing the sample from Step 3 into the high-pressure synthesis assembly block and place it in a six-sided top press for high-temperature and high-pressure reaction.

[0042] Step 5: After the high-temperature and high-pressure reaction is completed, the cylindrical tube wrapped in platinum foil is removed. A diamond cutter is used to cut the platinum tube, and the sample is extracted and ground to obtain yttrium content x = 0.10 silicate apatite powder (Ca).4.90 Y 0.10 )[(PO4) 2.90 (SiO3) 0.20 ]F.

[0043] The specific operation of the h-BN tube in step 3 is as follows: drill a 6mm hole in the center of an h-BN rod with a size of 10mm on a lathe to make an h-BN tube, insert the sample into the tube, and seal both ends with 6mm thick h-BN sheets.

[0044] The method for assembling the h-BN tube in the high-pressure synthesis assembly block as described in step 4 includes the following steps: selecting a pyrophyllite block and drilling a Φ12mm circular through hole in the center of the pyrophyllite block; fitting a circular graphite heating furnace with an outer diameter of 12mm and an inner diameter of Φ10mm inside the circular through hole; placing a 10mm h-BN tube-sealed sample in the middle of the graphite heating furnace; and sealing the upper and lower ends of the circular graphite heating furnace with pyrophyllite plugs.

[0045] The high-temperature and high-pressure reaction conditions described in step 4 are as follows: first, the pressure is increased to 3 GPa, then the temperature is increased to 1200℃, and the pressure and temperature are maintained for 2 hours before quenching.

[0046] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A high-temperature, high-pressure synthesis method for yttrium silicate apatite (Ca 5-x Y x )[(PO4) 3-x (SiO3) 2x The method of F is characterized in that, Includes the following steps: Step 1: Analytical grade calcium carbonate (CaCO3) and analytical grade nano-silica (SiO2) are mixed and ground evenly in a molar ratio of 1:

1. Using a powder press, the mixture powder is placed in a Φ10 mold and pressed into a cylindrical shape of Φ10mm×10mm. The cylindrical shape is then placed on a ceramic boat lined with platinum sheets and sintered in a silicon molybdenum rod furnace at 1000℃ for 12 hours. After natural cooling, it is ground, pressed, and sintered again at 1200℃ for 12 hours. The precursor calcium silicate (CaSiO3) powder is obtained by grinding. The synthesis reaction is: CaCO3 + SiO2 → CaSiO3 + CO2. Step 2: Analytical grade calcium phosphate Ca3(PO4)2 and analytical grade nano-calcium fluoride CaF2 are mixed and ground evenly at a molar ratio of 3:

1. Using a powder press, the mixture powder is placed in a Φ10mm mold and pressed into a Φ10mm×10mm cylindrical shape. The cylindrical shape is placed on a ceramic boat lined with platinum sheets and sintered in a silicon molybdenum rod furnace at 1000℃ for 24 hours. The precursor undoped apatite Ca5(PO4)3F powder is obtained by grinding. The synthesis reaction is: 3Ca3(PO4)2 + CaF2 → 2Ca5(PO4)3F. Step 3: The precursor phase calcium silicate (CaSiO3) synthesized in Steps 1 and 2, undoped apatite (Ca5(PO4)3F), analytical grade yttrium phosphate (YPO4), and analytical grade nano-calcium fluoride (CaF2) are mixed in molar proportions according to the left side of the reaction equation to obtain a mixture: (2-4x / 3)Ca5(PO4)3F + 2xYPO4 + 4xCaSiO3 + (2x / 3)CaF2 → 2(Ca 5-x Y x )[(PO4) 3-x (SiO3) 2x ]F, where x is the doping amount of rare earth yttrium Y. The mixture is ground evenly and then pressed into a Φ6mm×5mm cylinder using a powder presser. The cylinder is wrapped with a 0.02mm thick platinum foil and placed in an h-BN tube, with h-BN as the pressure transmission medium. Step 4: Assemble the h-BN tube containing the sample from Step 3 into the high-pressure synthesis assembly block and place it in a six-sided top press for high-temperature and high-pressure reaction. Step 5: After the high-temperature and high-pressure reaction is completed, the cylindrical tube wrapped in platinum foil is removed. A diamond cutter is used to cut the platinum tube, and the sample is extracted and ground to obtain yttrium silicate apatite powder (Ca). 5-x Y x )[(PO4) 3-x (SiO3) 2x ]F.

2. The high-temperature and high-pressure synthesis method for yttrium silicate apatite (Ca) according to claim 1. 5-x Y x )[(PO4) 3-x (SiO3) 2x The method of F is characterized in that, The specific operation of the h-BN tube in step 3 is as follows: drill a 6mm hole in the center of an h-BN rod with a size of 10mm on a lathe to make an h-BN tube, insert the sample into the tube, and seal both ends with 6mm thick h-BN sheets.

3. A high-temperature, high-pressure synthetic method for yttrium silicate apatite (Ca) according to claim 1. 5-x Y x )[(PO4) 3-x (SiO3) 2x The method of F is characterized in that, The method for assembling the h-BN tube in the high-pressure synthesis assembly block as described in step 4 includes the following steps: selecting a pyrophyllite block and drilling a Φ12mm circular through hole in the center of the pyrophyllite block; fitting a circular graphite heating furnace with an outer diameter of 12mm and an inner diameter of Φ10mm inside the circular through hole; placing a 10mm h-BN tube-sealed sample in the middle of the graphite heating furnace; and sealing the upper and lower ends of the circular graphite heating furnace with pyrophyllite plugs.

4. A high-temperature, high-pressure synthetic method for yttrium silicate apatite (Ca) according to claim 1. 5-x Y x )[(PO4) 3-x (SiO3) 2x The method of F is characterized in that, The high-temperature and high-pressure reaction conditions described in step 4 are as follows: first, the pressure is increased to 1-3 GPa, then the temperature is increased to 1050-1200℃, and the pressure and temperature are maintained for 2 hours before quenching.

5. A high-temperature, high-pressure synthetic method for yttrium silicate apatite (Ca) according to claim 1. 5-x Y x )[(PO4) 3-x (SiO3) 2x The method of F is characterized in that, The yttrium silicate apatite sample obtained in step 5 is a white powder, free of other impurities, with a monoclinic P63 / m crystal structure and lattice parameters [not specified]. α = 90°, β = 90°, γ = 120°, and the lattice parameters increase linearly with the increase of yttrium doping amount x.

6. A high-temperature, high-pressure synthetic method for yttrium silicate apatite (Ca) according to claim 1. 5-x Y x )[(PO4) 3-x (SiO3) 2x The method of F is characterized in that, The yttrium doping level x in the yttrium silicate apatite sample obtained in step 5 is in the range of 0. <x≤0.15。