Sodium ion battery hard carbon negative electrode material and preparation method and application thereof

Abstract

The application belongs to the technical field of sodium ion negative electrode material preparation, and particularly relates to a sodium ion battery hard carbon negative electrode material and a preparation method and application thereof. The method comprises the following steps: crushing biomass raw materials, sieving, acid washing and drying to obtain a low-ash biomass precursor powder, dispersing the biomass precursor powder in water, performing a hydrothermal reaction to obtain a pretreated biomass precursor powder, and finally placing the pretreated biomass precursor powder in a tube furnace with inert atmosphere protection to perform two-step heat treatment, so as to finally obtain a sodium ion battery hard carbon negative electrode material. The preparation method is simple and convenient to operate, the raw material is renewable biomass, and the method is energy-saving and environment-friendly. The biomass hard carbon negative electrode prepared by the acid pretreatment, hydrothermal regulation and two-step high-temperature calcination method has the advantages of high initial coulombic efficiency, good cycle performance and high rate performance and excellent sodium storage performance.

Description

Technical Field

[0001] This invention belongs to the field of sodium-ion anode material preparation technology, specifically relating to a hard carbon anode material for sodium-ion batteries, its preparation method, and its application. Background Technology

[0002] Sodium-ion batteries utilize abundant and inexpensive sodium resources, making them an ideal choice for large-scale energy storage applications. Developing high-performance, low-cost cathode and anode materials is crucial for the practical application of sodium-ion batteries. While alloyed and conversion-type anodes offer high capacity, they suffer from poor conductivity and severe volume expansion during the conversion or alloying process, hindering their commercialization in the short term. Hard carbon, with its low charge / discharge potential and high capacity, is considered the most suitable anode for commercial applications. The short-range ordered but long-range disordered graphite microcrystalline structure of hard carbon provides more defect sites, micropores, and sodium storage space. Simultaneously, the larger interlayer spacing of the graphite microcrystals facilitates rapid sodium ion diffusion. However, hard carbon anode materials currently suffer from low initial coulombic efficiency (ICE) and poor cycle stability, limiting their further large-scale industrial application in sodium-ion batteries. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a hard carbon anode material for sodium-ion batteries, its preparation method, and its application. Specifically, the following technical solution is adopted: In a first aspect, the present invention provides a method for preparing a hard carbon anode material for sodium-ion batteries, comprising the following steps: S1: After crushing the biomass raw material, sieve, acid wash, and dry it to obtain low-ash biomass precursor powder; S2: Disperse low-ash biomass precursor powder in an organic solvent and carry out a solvothermal reaction to obtain pretreated biomass precursor powder. S3: The pretreated biomass precursor powder is placed in a tube furnace with an inert atmosphere for two-step heat treatment to finally obtain the hard carbon anode material for sodium-ion batteries. The particle size distribution of the above-mentioned low-ash biomass precursor powder is D10 ≥ 2.0 μm, 4.0 μm ≤ D50 ≤ 15.0 μm, and D90 ≤ 45.0 μm; The ash content of the aforementioned low-ash biomass precursor powder is 0.1%-0.3%.

[0004] This invention uses renewable biomass as raw material, obtaining low-ash biomass precursor powder through crushing, sieving, and acid washing. Then, the low-ash biomass precursor powder is subjected to a solvothermal reaction to regulate the cellulose, hemicellulose, and lignin components, resulting in pretreated biomass precursor powder. This pretreated biomass precursor powder is then subjected to a two-step high-temperature calcination process to prepare a hard carbon anode material for sodium-ion batteries. Crushing and sieving ensure the uniformity of hard carbon particles, improving the electrochemical performance of the hard carbon; acid washing removes water-insoluble impurities from the precursor, reducing their impact on the battery; and the two-step high-temperature calcination method achieves a higher residual carbon rate compared to one-step calcination.

[0005] As a further preferred embodiment, the above-mentioned biomass raw material is at least one of coconut shell, walnut shell, pine nut shell, wood, and bamboo.

[0006] As a further preferred embodiment, the pickling solution used is a mixed acid solution composed of hydrochloric acid and nitric acid, wherein the volume ratio of hydrochloric acid, nitric acid, and water is 4:3:47. In this method, the mixed acid is more effective at removing ash than a single acid.

[0007] As a further preferred embodiment, the organic solvent in step S2 above includes one of alcohols, ketones, esters, ethers, phenols, and acids; The temperature of the solvothermal reaction is 120 ℃-280 ℃, and the time of the hydrothermal reaction is 4 h-24 h.

[0008] In this step, solvothermal treatment of biomass feedstock can regulate the cellulose and lignin composition of the biomass, improving batch-to-batch consistency of hard carbon. Compared to hydrothermal treatment, this method is more effective. Furthermore, excessively high solvothermal temperatures can have an undue impact on the biomass feedstock composition, while excessively low temperatures cannot achieve the desired regulatory effect. As a further preferred embodiment, the inert atmosphere in step S3 above is nitrogen or argon.

[0009] As a further preferred embodiment, the two-step heat treatment process of placing the pretreated biomass precursor powder in a tube furnace protected by an inert atmosphere is as follows: The heating rate of the first heat treatment is 5 ℃ / min-10 ℃ / min, the holding temperature is 500 ℃-700 ℃, and the holding time is 2 h-4 h; The second heat treatment involves a heating rate of 1 ℃ / min to 5 ℃ / min, a holding temperature of 1200 ℃ to 1500 ℃, and a holding time of 1 h to 3 h.

[0010] In the above heat treatment process, if the temperature of the first heat treatment step is too low, the carbonization will not be complete; if the temperature is too high, the energy consumption will be too high.

[0011] In a second aspect, the present invention provides a hard carbon anode material for sodium-ion batteries prepared by the above-described preparation method.

[0012] In a third aspect, the present invention also provides the application of the above-mentioned hard carbon anode material for sodium-ion batteries in the preparation of sodium-ion batteries.

[0013] In a fourth aspect, the present invention also provides a battery negative electrode sheet made from the above-mentioned sodium-ion battery hard carbon negative electrode material.

[0014] As a further preferred embodiment, the preparation process of the above-mentioned negative electrode sheet includes the following steps: The sodium-ion battery hard carbon anode material, conductive agent, binder and solvent are mixed and coated on a metal substrate, and then vacuum dried to obtain the battery anode sheet.

[0015] The beneficial effects of this invention are as follows: (1) The preparation method provided by the present invention is simple and easy to operate, and the raw material is renewable biomass, which is energy-saving and environmentally friendly. The biomass hard carbon anode prepared by the present invention through acid pretreatment combined with solvothermal regulation and two-step high-temperature calcination has the advantages of high initial coulombic efficiency, good cycle performance and high rate performance, which are excellent sodium storage performance.

[0016] (2) Compared with the hydrothermal method, the solvothermal method used in this invention can achieve precise control of cellulose, hemicellulose and lignin components in biomass precursors in a simple and efficient manner, which is beneficial to improving the batch consistency of biomass hard carbon products. Attached Figure Description

[0017] Figure 1 The figure shows the constant current cycling curve of the hard carbon anode material prepared in Example 1; Figure 2 The figure shows the constant current cycling curve of the hard carbon anode material prepared in Example 2; Figure 3 The figure shows the galvanostatic cycling curve of the hard carbon anode material prepared in Comparative Example 1. Figure 4 The figure shows the galvanostatic cycling curve of the hard carbon anode material prepared in Comparative Example 2. Detailed Implementation

[0018] The following will provide a clear and complete description of the concept, specific structure, and technical effects of the present invention in conjunction with the embodiments and accompanying drawings, so as to fully understand the purpose, solution, and effects of the present invention. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0019] Example 1 A method for preparing a hard carbon anode material for sodium-ion batteries, specifically including the following steps: Step 1: After crushing the biomass raw material walnut shell P1, sieve it, acid wash it (the volume ratio of concentrated hydrochloric acid, concentrated nitric acid and water is 4:3:47), and dry it at 80 ℃ for 4 h to obtain low ash biomass precursor walnut shell powder P2. Step 2: Weigh 5 g of the low-ash biomass precursor walnut shell powder P2 obtained above and disperse it in 50 mL of ethanol. Place it in a stainless steel reactor with a polytetrafluoroethylene liner and carry out a solvothermal reaction at 180 °C for 8 h to obtain pretreated biomass precursor walnut shell powder P3. Step 3: The pretreated biomass precursor walnut shell powder P3 obtained above is placed in a sagger and placed in a tube furnace under an inert atmosphere. The first heat treatment is performed from room temperature to 600 ℃ at a heating rate of 2 ℃ / min and held at the temperature for 2 h to obtain pre-carbonized walnut shell powder. The second heat treatment is performed from room temperature to 1400 ℃ at a heating rate of 5 ℃ / min and held at the temperature for 2 h to obtain sodium-ion battery hard carbon anode material C.

[0020] A button cell battery, the preparation method of which includes the following steps: The prepared hard carbon anode material B, super-p conductive agent, and polyvinylidene fluoride binder were mixed with N-methyl-2-pyrrolidone at a mass ratio of 8:1:1 to form a uniform slurry. This slurry was then uniformly coated onto copper foil using a coating method. After drying, the slurry was punched into circular electrode sheets and vacuum-dried at 120 °C for 12 h. Using the prepared hard carbon as the positive electrode, sodium metal sheet as the negative electrode, 1M NaClO4 and EC / DMC (volume ratio 1:1) as the electrolyte, and a glass fiber separator, a 2025 type button cell was assembled in a glove box. Cycle and rate performance tests were conducted on the button cell using a Newway battery tester (room temperature, voltage range 0.001-2V vs. Na / Na). + The result is as follows: Figure 1 As shown, the test results indicate that hard carbon material C can withstand a current density of 30 mA·g. -1 At that time, the initial specific capacity was 326.69 mAh·g. -1 The initial coulombic efficiency was 91.78%; at a current density of 150 mA·g -1 At that time, the specific capacity can reach 271.20 mAh·g after 100 cycles. -1 .

[0021] Example 2 A method for preparing a hard carbon anode material for sodium-ion batteries, specifically including the following steps: Step 1: After crushing the biomass raw material walnut shell P1, sieve it, acid wash it (the volume ratio of concentrated hydrochloric acid, concentrated nitric acid and water is 4:3:47), and dry it at 80 ℃ for 4 h to obtain low ash biomass precursor walnut shell powder P2. Step 2: Weigh 5 g of the low-ash biomass precursor walnut shell powder P2 obtained above and disperse it in 50 mL of acetone. Place it in a stainless steel reactor with a polytetrafluoroethylene liner and carry out a solvothermal reaction at 210 °C for 8 h to obtain pretreated biomass precursor walnut shell powder P3. Step 3: The pretreated biomass precursor walnut shell powder P3 obtained above is placed in a sagger and placed in a tube furnace under an inert atmosphere. The first heat treatment is performed from room temperature to 600 ℃ at a heating rate of 2 ℃ / min and held at the temperature for 2 h to obtain pre-carbonized walnut shell powder. The second heat treatment is performed from room temperature to 1400 ℃ at a heating rate of 5 ℃ / min and held at the temperature for 2 h to obtain sodium-ion battery hard carbon anode material D.

[0022] A button cell battery, the preparation method of which includes the following steps: The prepared hard carbon anode material C, super-p conductive agent, and polyvinylidene fluoride binder were mixed with N-methyl-2-pyrrolidone at a mass ratio of 8:1:1 to form a uniform slurry. This slurry was then uniformly coated onto copper foil using a coating method. After drying, the slurry was punched into circular electrode sheets and vacuum-dried at 120 °C for 12 h. Using the prepared hard carbon as the positive electrode, sodium metal sheet as the negative electrode, 1M NaClO4 and EC / DMC (volume ratio 1:1) as the electrolyte, and a glass fiber separator, a 2025 type button cell was assembled in a glove box. Cycle and rate performance tests were conducted on the button cell using a Newway battery tester (room temperature, voltage range 0.001-2V vs. Na / Na). + The result is as follows: Figure 2 As shown, the test results indicate that hard carbon material D, at a current density of 30 mA·g -1 At that time, the initial specific capacity was 331.68 mAh·g. -1 The initial coulombic efficiency was 92.07%; at a current density of 150 mA·g -1 At that time, the specific capacity can reach 282.44 mAh·g after 100 cycles. -1 .

[0023] Example 3 A method for preparing a hard carbon anode material for sodium-ion batteries. The specific preparation process in this embodiment is only that acetone in step 2 of Example 2 is replaced with ethylene glycol, and the remaining steps are exactly the same as in Example 2, resulting in a hard carbon anode material E.

[0024] A button cell battery, the preparation method of which includes the following steps: The prepared hard carbon anode material D, super-p conductive agent, and polyvinylidene fluoride binder were mixed with N-methyl-2-pyrrolidone at a mass ratio of 8:1:1 to form a uniform slurry. This slurry was then uniformly coated onto copper foil using a coating method. After drying, the slurry was punched into circular electrode sheets and vacuum-dried at 120 °C for 12 h. Using the prepared hard carbon as the positive electrode, sodium metal sheet as the negative electrode, 1M NaClO4 and EC / DMC (volume ratio 1:1) as the electrolyte, and a glass fiber separator, a 2025 type button cell was assembled in a glove box. Cycle and rate performance tests were conducted on the button cell using a Newway battery tester (room temperature, voltage range 0.001-2V vs. Na / Na). + Test results show that hard carbon material E operates at a current density of 30 mA·g. -1 At that time, the initial specific capacity was 343.68 mAh·g. -1 The initial Coulomb efficiency was 90.34%.

[0025] Example 4 A method for preparing a hard carbon anode material for sodium-ion batteries. The specific preparation process in this embodiment is only that acetone in step 2 of Example 2 is replaced with acetic acid, and the remaining steps are exactly the same as in Example 2, resulting in a hard carbon anode material F.

[0026] A button cell battery, the preparation method of which includes the following steps: The prepared hard carbon anode material E, super-p conductive agent, and polyvinylidene fluoride binder were mixed with N-methyl-2-pyrrolidone at a mass ratio of 8:1:1 to form a uniform slurry. This slurry was then uniformly coated onto copper foil using a coating method. After drying, the slurry was punched into circular electrode sheets and vacuum-dried at 120 °C for 12 h. Using the prepared hard carbon as the positive electrode, sodium metal sheet as the negative electrode, 1M NaClO4 and EC / DMC (volume ratio 1:1) as the electrolyte, and a glass fiber separator, a 2025 type button cell was assembled in a glove box. Cycle and rate performance tests were conducted on the button cell using a Newway battery tester (room temperature, voltage range 0.001-2V vs. Na / Na). + Test results show that hard carbon material F can withstand current densities of 30 mA·g. -1 At that time, the initial specific capacity was 325.57 mAh·g. -1 The initial Coulomb efficiency was 91.29%.

[0027] Example 5 A method for preparing a hard carbon anode material for sodium-ion batteries. The specific preparation process in this embodiment is only that the walnut shell in step 1 of embodiment 3 is replaced with bamboo powder. The remaining steps are exactly the same as in embodiment 3, and the hard carbon anode material G is obtained.

[0028] A button cell battery, the preparation method of which includes the following steps: The prepared hard carbon anode material F, super-p conductive agent, and polyvinylidene fluoride binder were mixed with N-methyl-2-pyrrolidone at a mass ratio of 8:1:1 to form a uniform slurry. This slurry was then uniformly coated onto copper foil using a coating method. After drying, the slurry was punched into circular electrode sheets and vacuum-dried at 120 °C for 12 h. Using the prepared hard carbon as the positive electrode, sodium metal sheet as the negative electrode, 1M NaClO4 and EC / DMC (volume ratio 1:1) as the electrolyte, and a glass fiber separator, a 2025 type button cell was assembled in a glove box. Cycle and rate performance tests were conducted on the button cell using a Newway battery tester (room temperature, voltage range 0.001-2V vs. Na / Na). + Test results show that hard carbon material E operates at a current density of 30 mA·g. -1 At that time, the initial specific capacity was 321.59 mAh·g. -1 The initial Coulomb efficiency was 89.9%.

[0029] Example 6 A method for preparing a hard carbon anode material for sodium-ion batteries. The specific preparation process in this embodiment is only that the walnut shell in step 1 of embodiment 3 is replaced with poplar wood powder. The remaining steps are exactly the same as in embodiment 3, and the hard carbon anode material obtained is H.

[0030] A button cell battery, the preparation method of which includes the following steps: The hard carbon anode material H, super-p conductive agent, and polyvinylidene fluoride binder obtained by solvothermal combined with high-temperature calcination were mixed with N-methyl-2-pyrrolidone at a mass ratio of 8:1:1 to form a uniform slurry. This slurry was then uniformly coated onto copper foil using a coating method. After drying, the slurry was punched into circular electrode sheets and vacuum-dried at 120°C for 12 hours. Using the prepared hard carbon as the positive electrode, sodium metal sheet as the negative electrode, 1M NaClO4 and EC / DMC (volume ratio 1:1) as the electrolyte, and a glass fiber separator, a 2025 type button cell was assembled in a glove box. Cycle and rate performance tests were conducted on the button cell using a Newway battery tester (room temperature, voltage range 0.001-2V vs. Na / Na). + Test results show that hard carbon material F can withstand current densities of 30 mA·g. -1 At that time, the initial specific capacity was 339.87 mAh·g. -1 The initial Coulomb efficiency was 90.23%.

[0031] Comparative Example 1 A method for preparing a hard carbon anode material for sodium-ion batteries, specifically including the following steps: Step 1: After crushing the biomass raw material walnut shell P1, sieve it, acid wash it, and dry it at 80 ℃ for 4 h to obtain low ash biomass precursor walnut shell powder P2. Step 2: Weigh 5 g of the above P2 powder and place it in a crucible. Then place it in a tube furnace with an inert atmosphere. Perform the first heat treatment from room temperature to 600 ℃ at a heating rate of 2 ℃ / min and hold for 2 h to obtain pre-carbonized walnut shell powder. Perform the second heat treatment from room temperature to 1400 ℃ at a heating rate of 5 ℃ / min and hold for 2 h to obtain sodium-ion battery hard carbon anode material A.

[0032] A button cell battery, the preparation method of which includes the following steps: The prepared hard carbon anode material, super-p conductive agent, and polyvinylidene fluoride binder were mixed with N-methyl-2-pyrrolidone at a mass ratio of 8:1:1 to form a uniform slurry. This slurry was then uniformly coated onto copper foil using a coating method. After drying, the slurry was punched into circular electrode sheets and vacuum-dried at 120 °C for 12 h. Using the prepared hard carbon as the positive electrode, sodium metal as the negative electrode, 1M NaClO4 and EC / DMC (volume ratio 1:1) as the electrolyte, and a glass fiber separator, a 2025 type button cell was assembled in a glove box. Cycle and rate performance tests were conducted on the button cell using a Newway battery tester (room temperature, voltage range 0.001-2V vs. Na / Na). + The result is as follows: Figure 3 As shown, the test results indicate that hard carbon material A, at a current density of 30 mA·g -1 At that time, the initial specific capacity was 303.51 mAh·g. -1 The initial coulombic efficiency was 88.99%; at a current density of 150 mA·g -1 At that time, the specific capacity can reach 238.79 mAh·g after 100 cycles. -1 .

[0033] Comparative Example 2 A method for preparing a hard carbon anode material for sodium-ion batteries, specifically including the following steps: Step 1: After crushing the biomass raw material walnut shell P1, sieve it, acid wash it, and dry it at 80 ℃ for 4 h to obtain low ash biomass precursor walnut shell powder P2. Step 2: Weigh 5 g of the above low-ash biomass precursor walnut shell powder P2 and disperse it in 50 mL of water. Place it in a stainless steel reactor with a polytetrafluoroethylene liner and carry out a hydrothermal reaction at 180 °C for 8 h to obtain pretreated biomass precursor walnut shell powder P3. Step 3: The above-mentioned biomass precursor walnut shell powder P3 is placed in a sagger and placed in a tube furnace under an inert atmosphere. The first heat treatment is performed from room temperature to 600 ℃ at a heating rate of 2 ℃ / min and held at the temperature for 2 h to obtain pre-carbonized walnut shell powder. The second heat treatment is performed from room temperature to 1400 ℃ at a heating rate of 5 ℃ / min and held at the temperature for 2 h to obtain sodium-ion battery hard carbon anode material A.

[0034] A button cell battery, the preparation method of which includes the following steps: The hard carbon anode material B obtained by hydrothermal combined with high-temperature calcination, super-p conductive agent, and polyvinylidene fluoride binder were mixed with N-methyl-2-pyrrolidone at a mass ratio of 8:1:1 to form a uniform slurry. This slurry was then uniformly coated onto copper foil using a coating method. After drying, the slurry was punched into circular electrode sheets and vacuum-dried at 120°C for 12 hours. Using the prepared hard carbon as the positive electrode, sodium metal sheet as the negative electrode, 1M NaClO4 and EC / DMC (volume ratio 1:1) as the electrolyte, and a glass fiber separator, a 2025 type button cell was assembled in a glove box. Cycle and rate performance tests were conducted on the button cell using a Newway battery tester (room temperature, voltage range 0.001-2V vs. Na / Na). + The result is as follows: Figure 4 As shown, the test results indicate that hard carbon material B operates at a current density of 30 mA·g. -1 At that time, the initial sodium intercalation capacity was 310.82 mAh·g. -1 The initial coulombic efficiency was 89.17%; at a current density of 150 mA·g -1 At that time, the specific capacity can reach 263.55 mAh·g after 100 cycles. -1 .

[0035] Table 1 compares the electrochemical performance of the sodium-ion battery hard carbon anode materials prepared in Examples 1-5 and Comparative Example 1. Table 1 Comparison of Electrochemical Performance of Materials As shown in the table above, hydrothermal preparation of hard carbon exhibits higher electrochemical performance than non-hydrothermal preparation, while organic solvothermal preparation of hard carbon is more effective than simple hydrothermal treatment. Organic solvents are also effective for different biomass raw materials.

[0036] Although the description of the invention has been quite detailed and particularly of several described embodiments, it is not intended to limit it to any of these details or embodiments or any particular embodiment, but should be considered as providing a broad possible interpretation of the claims by referring to the appended claims and taking into account the prior art, thereby effectively covering the intended scope of the invention. Furthermore, the invention has been described above with respect to embodiments foreseeable by the inventors in order to provide a useful description, and non-substantial modifications to the invention that have not yet been foreseen may still represent equivalent modifications.

Claims

1. A method for preparing a hard carbon anode material for sodium-ion batteries, characterized in that, Includes the following steps: S1: After crushing the biomass raw material, it is sieved and then acid-washed with a mixed acid solution of hydrochloric acid, nitric acid and water, wherein the volume ratio of hydrochloric acid, nitric acid and water is 4:3:

47. After drying, a low-ash biomass precursor powder is obtained. S2: The low-ash biomass precursor powder is dispersed in an organic solvent including one of alcohols, ketones, esters, ethers, phenols, and acids, and a solvothermal reaction is carried out at a temperature of 120 °C. 280 ℃, for 4 hours After 24 hours, pretreated biomass precursor powder was obtained; S3: The pretreated biomass precursor powder is placed in a tube furnace under inert atmosphere protection for a two-step heat treatment. The two-step heat treatment process is as follows: the first heat treatment has a heating rate of 5 °C / min - 10 °C / min, a holding temperature of 500 °C - 700 °C, and a holding time of 2 h. The second heat treatment involves a heating rate of 1 °C / min - 5 °C / min, a holding temperature of 1200 °C - 1500 °C, and a holding time of 1 h. 3 h; finally, a hard carbon anode material for sodium-ion batteries was obtained; The low-ash biomass precursor powder has a particle size distribution of D10 ≥ 2.0 μm, 4.0 μm ≤ D50 ≤ 15.0 μm, and D90 ≤ 45.0 μm; The ash content of the low-ash biomass precursor powder is 0.1%-0.3%.

2. The preparation method according to claim 1, characterized in that, The biomass raw material is at least one of coconut shell, walnut shell, pine nut shell, wood, and bamboo.

3. The preparation method according to claim 1, characterized in that, In step S3, the inert atmosphere is nitrogen or argon.

4. A hard carbon anode material for sodium-ion batteries, characterized in that, It is prepared by the preparation method according to any one of claims 1-3.

5. The application of the sodium-ion battery hard carbon anode material according to claim 4 in the preparation of sodium-ion batteries.

6. A battery negative electrode sheet, characterized in that, It is prepared from the sodium-ion battery hard carbon anode material as described in claim 4.

7. The battery negative electrode sheet according to claim 6, characterized in that, The preparation process includes the following steps: The sodium-ion battery hard carbon anode material, conductive agent, binder and solvent are mixed and coated on a metal substrate, and then vacuum dried to obtain the battery anode sheet.

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