A cathode for rare earth molten salt electrolysis and an electrolysis system comprising the same

Abstract

This disclosure provides a cathode comprising: a column having a conical base and a pointed or flat apex; wherein when the apex of the cone is a pointed angle, the angle of the pointed angle is between 5 degrees and 175 degrees; this disclosure also provides an electrolysis system including the cathode.

Description

Technical Field

[0001] The present disclosure relates to a cathode and an electrolysis system comprising the same, and in particular to a cathode for rare earth molten salt electrolysis and an electrolysis system comprising the same. Prior Art

[0002] Rare earth elements (REEs) play a crucial role in improving product performance and have a wide range of applications, including permanent magnets, ceramics and glass, optoelectronics, catalytic materials, superconductors, and green energy. However, in the molten salt electrolysis process of rare earth fluorides, in addition to producing carbon monoxide and carbon dioxide, high anode current densities can also generate fluorine gas and fluorocarbons, contributing to greenhouse gas emissions. Therefore, the electrode structure and electrode configuration of the molten salt electrolysis process need to be optimized to reduce the local cathode current density and the anode current density to increase rare earth metal yields. Summary of the Invention

[0003] According to one embodiment of the present disclosure, a cathode for preparing rare earth metals by rare earth molten salt electrolysis is provided, comprising: a column having a conical bottom and a pointed or flat top; wherein when the pointed top is a pointed angle, the angle of the pointed angle is between 5 degrees and 175 degrees.

[0004] In one embodiment, the cathode is composed of tungsten, molybdenum, or tantalum.

[0005] In one embodiment, when the sides of the cone are the same length, the angle of the tip is calculated using the formula (I): c² = 2a²(1-cos(γ)), where c is the diameter of the cylinder, a is the length of the side of the cone, and γ is the angle of the tip. In one embodiment, the sides of the cone are of different lengths.

[0006] According to one embodiment of the present disclosure, an electrolysis system is provided, comprising: a cathode; at least one anode; and an electrolyte comprising a rare earth oxide, wherein the cathode and the anode are disposed in the electrolyte. The ratio of the surface area of the cathode to the surface area of the anode is between 1:100 and 1:1.

[0007] In one embodiment, the cathode comprises a column. In one embodiment, the bottom of the cathode comprises a flat surface, an arc shape, or a cone shape.

[0008] In one embodiment, the conical tip includes a sharp angle or is flat. In one embodiment, when the conical tip is sharp, the angle of the angle is between 5 degrees and 175 degrees. In one embodiment, when the conical tip is sharp and the lengths of the sides of the cone are the same, the angle of the angle is calculated using the formula (I): c²=2a²(1-cos(γ)), where c is the diameter of the cylinder, a is the length of the side of the cone, and γ is the angle of the angle. In one embodiment, the conical tip is sharp and the lengths of the sides of the cone are different.

[0009] In one embodiment, at least one anode surrounds the cathode.

[0010] In one embodiment, the cathode is composed of tungsten, molybdenum, or tantalum. In one embodiment, at least one anode is composed of graphite.

[0011] In one embodiment, the rare earth oxide includes neodymium oxide, ferroxene oxide, or dysprosium oxide.

[0012] This disclosure utilizes a fluoride / rare earth molten salt electrolyte system, with a graphite anode and a tungsten, molybdenum, or tantalum cathode in a cylindrical, conical, or combination thereof shape. The cathode is placed in the center of the crucible, while the anodes are positioned around or symmetrically around the cathode. Once current is applied, an electrolysis reaction occurs. During the electrolysis process, because the melting point of the generated rare earth metal is lower than that of the cathode, the surface of the cathode is first electrolyzed into metal droplets, which then fall into the crucible at the bottom.

[0013] When the particle size of the obtained rare earth metal increases, the specific surface area decreases proportionally. This phenomenon can greatly reduce metal oxidation and improve electrolysis efficiency.

[0014] The size and shape of the cathode affect the local current density, causing the reduced metal to form droplets of varying sizes. For example, at the same current density, current concentration at the electrode tip increases the local current density, which in turn increases the amount of metal deposited and the diameter of the metal droplets, making them easier to collect and achieving high electrolysis efficiency.

[0015] The main technology disclosed herein utilizes electrolytic electrode design in a fluorine-containing molten salt metal electrolysis system to improve the electrolytic metal recovery rate and reduce the anode current density, thereby preventing the decomposition of the fluoride salt electrolyte to produce fluorine gas / fluoride, thereby depositing and concentrating rare earth metals and increasing metal yield. Simple diagram description

[0016] FIG1A is a schematic diagram of an electrolysis system according to one embodiment of the present disclosure; FIG1B is a schematic diagram of an electrolysis system according to one embodiment of the present disclosure; FIG2A is a cross-sectional schematic diagram of a cathode structure in an electrolysis system according to one embodiment of the present disclosure; FIG2B is a cross-sectional schematic diagram of a cathode structure in an electrolysis system according to one embodiment of the present disclosure; FIG2C is a cross-sectional schematic diagram of a cathode structure in an electrolysis system according to one embodiment of the present disclosure; FIG2D is a cross-sectional schematic diagram of a cathode structure in an electrolysis system according to one embodiment of the present disclosure; FIG. 3 is a graph showing the relationship between product particle size and current efficiency obtained by different electrolysis systems according to one embodiment of the present disclosure. Implementation Method

[0017] The following disclosure provides many different embodiments for implementing different features of the present invention.

[0018] In the specification, the terms "about", "approximately", "roughly", "substantially", "same", and "similar" generally indicate that a characteristic value is within a range of plus or minus 15%, plus or minus 10%, plus or minus 5%, plus or minus 3%, plus or minus 2%, plus or minus 1%, or plus or minus 0.5% of a given value. The quantities given here are approximate quantities, that is, even if "about", "approximately", "roughly", "substantially" is not specifically stated, the meaning of "about", "approximately", "roughly", "substantially" can still be implied.

[0019] Unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meanings as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It is understood that these terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning consistent with the background or context of the relevant technology and the present invention, and should not be interpreted in an idealized or overly formal manner unless specifically defined in the embodiments of the present invention.

[0020] 1A , according to one embodiment of the present disclosure, an electrolysis system 10 is provided. FIG. 1A is a schematic diagram of the electrolysis system 10 .

[0021] As shown in FIG. 1A , electrolysis system 10 includes a cathode 12, an anode 14, and an electrolyte (not shown). Cathode 12 is composed of tungsten, molybdenum, or tantalum. Anode 14 is composed of graphite. The electrolyte contains a rare earth oxide. Cathode 12 and anode 14 are disposed within the electrolyte. The ratio of the surface area of cathode 12 to the surface area of anode 14 is between 1:100 and 1:1.

[0022] Referring to FIG. 1B , an electrolysis system 10 is provided according to one embodiment of the present disclosure. FIG. 1B is a schematic diagram of the electrolysis system 10 .

[0023] As shown in FIG. 1B , electrolysis system 10 includes a cathode 12, a plurality of anodes 14, and an electrolyte (not shown). Cathode 12 is composed of tungsten, molybdenum, or tantalum. Anode 14 is composed of graphite and surrounds cathode 12. The electrolyte comprises a rare earth oxide. Cathode 12 and anode 14 are disposed within the electrolyte. The ratio of the surface area of cathode 12 to the surface area of anode 14 is between 1:100 and 1:1.

[0024] 2A to 2D further illustrate the shape of the cathode 12 in the electrolysis system 10 according to one embodiment of the present disclosure. 2A to 2D are schematic cross-sectional views of the cathode 12.

[0025] As shown in FIG. 2A , in one embodiment, the cathode 12 is a column, and the bottom 12B of the cathode 12 is a plane.

[0026] As shown in FIG. 2B , in one embodiment, the cathode 12 is a column, and the bottom 12B of the cathode 12 is arc-shaped.

[0027] As shown in FIG. 2C , in one embodiment, the cathode 12 is a column, the bottom 12B of the cathode 12 is conical, and the top 12Bb of the conical bottom 12B is a sharp corner.

[0028] As shown in FIG. 2C , in one embodiment, when the top 12Bb of the bottom 12B of the cathode 12 is a sharp angle, the angle γ of the sharp angle is greater than 0 degrees and less than 180 degrees, for example, between 5 degrees and 175 degrees. In one embodiment, when the top 12Bb of the bottom 12B of the cathode 12 is a sharp angle, and the length a of the side 12B' of the conical bottom 12B is the same as the length b of the side 12B", the angle γ of the sharp angle is calculated by the following formula (I).

[0029] c 2=2a 2(1-cos(γ)) (I)

[0030] In formula (I), c is the diameter of the cathode 12, a is the length of the side 12B' of the conical bottom 12B, and γ is the angle of the tip.

[0031] In one embodiment, the top 12Bb of the bottom 12B of the cathode 12 is a sharp corner, and the length a of the side 12B′ of the conical bottom 12B is different from the length b of the side 12B″ (not shown).

[0032] As shown in FIG. 2D , the cathode 12 is a column, the bottom 12B of the cathode 12 is conical, and the top 12Bb of the conical bottom 12B is flat.

[0033] The shape of the cathode 12 disclosed in the present disclosure is not limited to the shapes shown in Figures 2A to 2D. Other suitable columnar, conical, or combined structures are also applicable to the present disclosure.

[0034] In one embodiment, the rare earth oxide in the electrolyte includes neodymium oxide, ferroxene oxide, or dysprosium oxide.

[0035] Example

[0036] A rare earth oxide (e.g., neodymium oxide (Nd2O3)) is added to an electrolyte containing a rare earth fluoride (e.g., neodymium fluoride (NdF3)) and lithium fluoride (LiF). This electrolyte is then placed in a graphite crucible. The crucible is then placed in a sealed metal chamber protected by an inert gas atmosphere. The chamber is heated to above 1,050°C and electrolysis is performed using graphite as the anode and tungsten as the cathode. Neodymium metal is produced on the tungsten electrode or in the electrolyte.

[0037] Example 1

[0038] Neodymium metal is prepared using the disclosed electrolytic system (cathode: columnar structure with a flat bottom).

[0039] Neodymium oxide (1.5 wt%) is added to an electrolyte containing 90% neodymium fluoride and 10% lithium fluoride. This electrolyte is then placed in a graphite crucible. The crucible is then placed in a sealed metal chamber protected by an inert gas (Ar). The crucible is heated to 1050°C and electrolyzed using graphite as the anode and tungsten as the cathode. Neodymium metal is deposited on the tungsten electrode or in the electrolyte.

[0040] The anode has a diameter of 10 mm and a length of 150 mm. The cathode has a diameter of 10 mm and a length of 150 mm. The cathode has a cylindrical structure with a flat bottom. The ratio of the cathode surface area to the anode surface area is 1:1. The electrodes are immersed in the electrolyte to a depth of 50 mm. The current density is 150 ASD. The electrolysis time is 2 hours. The tungsten electrode diameter, maximum product particle size, and specific surface area are listed in Table 1 below. Table 1 Tungsten electrode diameter (mm) Maximum particle size of product (mm) Specific surface area (cm 2 / g) 10 6~7 0.69~1.01

[0041] According to Table 1, after electrolysis using the electrolysis system of this embodiment (cathode: columnar structure, flat bottom, 10 mm diameter), the maximum particle size of the neodymium metal obtained was between approximately 6 mm and approximately 7 mm, and its specific surface area was between approximately 0.69 cm² / g and approximately 1.01 cm² / g.

[0042] Example 2

[0043] Neodymium metal is prepared using the disclosed electrolytic system (cathode: columnar structure with a flat bottom).

[0044] Neodymium oxide (1.5 wt%) is added to an electrolyte containing 90% neodymium fluoride and 10% lithium fluoride. This electrolyte is then placed in a graphite crucible. The crucible is then placed in a sealed metal chamber protected by an inert gas (Ar). The crucible is heated to 1050°C and electrolyzed using graphite as the anode and tungsten as the cathode. Neodymium metal is deposited on the tungsten electrode or in the electrolyte.

[0045] The anode had a diameter of 10 mm and a length of 150 mm. The cathode had a diameter of 3.2 mm and a length of 150 mm. The cathode had a cylindrical structure with a flat bottom. The ratio of the cathode surface area to the anode surface area was 1:3.16. The electrodes were immersed in the electrolyte to a depth of 50 mm. The current density was 150 ASD. The electrolysis time was 2 hours. The tungsten electrode diameter, maximum product particle size, and specific surface area are listed in Table 2 below. Table 2 Tungsten electrode diameter (mm) Maximum particle size of product (mm) Specific surface area (cm 2 / g) 3.2 15~16 0.48~0.51

[0046] According to Table 2, after electrolysis using the electrolysis system of this embodiment (cathode: columnar structure, flat bottom, 3.2 mm diameter), the maximum particle size of the neodymium metal obtained was between approximately 15 mm and approximately 16 mm, and its specific surface area was between approximately 0.48 cm² / g and approximately 0.51 cm² / g.

[0047] It can be seen from the results shown in Tables 1 and 2 that when the diameter of the tungsten electrode in the electrolysis system is reduced from 10 mm to 3.2 mm, the maximum particle size of the obtained neodymium metal becomes significantly larger and the specific surface area becomes significantly smaller, which will help reduce the oxidation of neodymium metal and improve the electrolysis efficiency.

[0048] Example 3

[0049] Neodymium metal is prepared using the disclosed electrolytic system (cathode: a combined columnar and conical structure with a pointed bottom).

[0050] Neodymium oxide (1.5 wt%) is added to an electrolyte containing 90% neodymium fluoride and 10% lithium fluoride. This electrolyte is then placed in a graphite crucible. The crucible is then placed in a sealed metal chamber protected by an inert gas (Ar). The crucible is heated to 1050°C and electrolyzed using graphite as the anode and tungsten as the cathode. Neodymium metal is deposited on the tungsten electrode or in the electrolyte.

[0051] The anode has a diameter of 10 mm and a length of 150 mm. The cathode has a diameter of 3.2 mm and a length of 150 mm. The cathode has a columnar structure with a pointed bottom. The taper angle is calculated using formula (I). The ratio of the cathode surface area to the anode surface area is 1:3.42. The electrode is immersed in the electrolyte to a depth of 50 mm. The current density is 150 ASD. The electrolysis time is 2 hours. The tungsten electrode diameter, maximum product particle size, and specific surface area are listed in Table 3 below. Table 3 Tungsten electrode diameter (mm) Maximum particle size of product (mm) Specific surface area (cm 2 / g) 3.2 16~18 0.37~0.48

[0052] According to Table 3, after electrolysis using the electrolysis system of this embodiment (cathode: a combined columnar and conical structure with a pointed bottom and a diameter of 3.2 mm), the maximum particle size of the neodymium metal obtained ranged from approximately 16 mm to approximately 18 mm, and its specific surface area ranged from approximately 0.37 cm² / g to approximately 0.48 cm² / g.

[0053] The results shown in Tables 2 and 3 show that when the bottom structure of the tungsten electrode in the electrolysis system is changed from a flat surface to a pointed tip, the current concentration and local current density increase at the electrode tip can further increase the diameter of the resulting metal droplets and further reduce the specific surface area. This can increase the amount of metal electrolytic precipitation, make it easier to collect metal droplets, and achieve high electrolysis efficiency.

[0054] Example 4

[0055] Neodymium metal is prepared using the disclosed electrolytic system (cathode: columnar structure with a flat bottom).

[0056] Neodymium oxide (2.0 wt%) is added to an electrolyte containing 76% neodymium fluoride, 20% lithium fluoride, and 4% barium fluoride. This electrolyte is then placed in a graphite crucible. The crucible is then placed in a sealed metal chamber protected by an inert gas (Ar). The crucible is heated to 1050°C and electrolyzed using graphite as the anode and tungsten as the cathode. Neodymium metal is deposited on the tungsten electrode or in the electrolyte.

[0057] The anode had a diameter of 10 mm and a length of 150 mm. The cathode had a diameter of 6.5 mm and a length of 150 mm. The cathode had a cylindrical structure with a flat bottom. The ratio of the cathode surface area to the anode surface area was 1:1.58. The electrodes were immersed in the electrolyte to a depth of 30 mm. The current density was 120 ASD. The electrolysis time was 2 hours. The tungsten electrode diameter, maximum product particle size, and specific surface area are listed in Table 4 below. Table 4 Tungsten electrode diameter (mm) Maximum particle size of product (mm) Specific surface area (cm 2 / g) 6.5 7~9 0.96~1.24

[0058] According to Table 4, after electrolysis using the electrolysis system of this embodiment (cathode: columnar structure, flat bottom, 6.5 mm diameter), the maximum particle size of the neodymium metal obtained ranged from approximately 7 mm to approximately 9 mm, and its specific surface area ranged from approximately 0.96 cm² / g to approximately 1.24 cm² / g.

[0059] Example 5

[0060] Neodymium metal is prepared using the disclosed electrolytic system (cathode: columnar structure with a flat bottom).

[0061] Neodymium oxide (2.0 wt%) is added to an electrolyte containing 76% neodymium fluoride, 20% lithium fluoride, and 4% barium fluoride. This electrolyte is then placed in a graphite crucible. The crucible is then placed in a sealed metal chamber protected by an inert gas (Ar). The crucible is heated to 1050°C and electrolyzed using graphite as the anode and tungsten as the cathode. Neodymium metal is deposited on the tungsten electrode or in the electrolyte.

[0062] The anode had a diameter of 10 mm and a length of 150 mm. The cathode had a diameter of 3.2 mm and a length of 150 mm. The cathode had a cylindrical structure with a flat bottom. The ratio of the cathode surface area to the anode surface area was 1:3.29. The electrodes were immersed in the electrolyte to a depth of 30 mm. The current density was 120 ASD. The electrolysis time was 2 hours. The tungsten electrode diameter, maximum product particle size, and specific surface area are listed in Table 5 below. Table 5 Tungsten electrode diameter (mm) Maximum particle size of product (mm) Specific surface area (cm 2 / g) 3.2 14~15 0.58~0.62

[0063] According to Table 5, after electrolysis using the electrolysis system of this embodiment (cathode: columnar structure, flat bottom, 3.2 mm diameter), the maximum particle size of the neodymium metal obtained was between approximately 14 mm and approximately 15 mm, and its specific surface area was between approximately 0.58 cm² / g and approximately 0.62 cm² / g.

[0064] The results shown in Tables 4 and 5 indicate that when the electrolyte composition is adjusted (for example, by adding barium fluoride), if the diameter of the tungsten electrode continues to decrease from 6.5 mm to 3.2 mm, the maximum particle size of the resulting neodymium metal will still increase, while the specific surface area will still decrease. In other words, during the electrolysis process, adjusting the electrolyte composition has a relatively small impact on the electrolysis efficiency, while the cathode size is one of the key factors that determine whether the electrolysis efficiency can be further improved.

[0065] Example 6

[0066] The relationship between product particle size and current efficiency obtained in different electrolysis systems (different cathode sizes and shapes).

[0067] In this example, electrolysis reactions were performed using different electrolysis systems (I, II, III, and IV). The relationship between the particle size of the resulting product and the current efficiency is shown in Table 6 and Figure 3 below. Figure 3 shows the relationship between the particle size of the product and the current efficiency obtained using different electrolysis systems.

[0068] Electrolysis system I: The electrolysis system as described in Example 1 (cathode: columnar structure, flat bottom, diameter 10 mm).

[0069] Electrolysis system II: the electrolysis system as shown in Example 4 (cathode: columnar structure, flat bottom, diameter 6.5 mm).

[0070] Electrolysis system III: the electrolysis system as shown in Example 5 (cathode: columnar structure, flat bottom, diameter 3.2 mm).

[0071] Electrolysis system IV: the electrolysis system as described in Example 3 (cathode: a combined columnar and conical structure with a pointed bottom and a diameter of 3.2 mm). Table 6 Cathode diameter (mm) Product particle size (mm) Current efficiency (%) 10 (flat bottom) 6 47.4 6.5 (flat bottom) 8 50 3.2 (flat bottom) 14 51 3.2 (bottom is pointed) 16 71

[0072] Table 6 and the results shown in Figure 3 show that as the tungsten electrode diameter decreases from 10 mm to 3.2 mm, the resulting neodymium metal particle size gradually increases (6 mm, 8 mm, 14 mm), and the current efficiency gradually improves (47.4%, 50%, 51%). Furthermore, when the bottom structure of the tungsten electrode changes from a flat surface (as shown in electrolysis system III) to a pointed tip (as shown in electrolysis system IV), the resulting metal droplet diameter increases further to 16 mm, and the current efficiency increases further to 71%.

[0073] This disclosure utilizes a fluoride / rare earth molten salt electrolyte system, with a graphite anode and a tungsten, molybdenum, or tantalum cathode in a cylindrical, conical, or combination thereof shape. The cathode is placed in the center of the crucible, while the anodes are positioned around or symmetrically around the cathode. Once current is applied, an electrolysis reaction occurs. During the electrolysis process, because the melting point of the generated rare earth metal is lower than that of the cathode, the surface of the cathode is first electrolyzed into metal droplets, which then fall into the crucible at the bottom.

[0074] The size and shape of the cathode affect the local current density, causing the reduced metal to form droplets of varying sizes. For example, at the same current density, current concentration at the electrode tip increases the local current density, which in turn increases the amount of metal deposited and the diameter of the metal droplets, making them easier to collect and achieving high electrolysis efficiency.

[0075] When the particle size of the obtained rare earth metal increases, the specific surface area decreases proportionally. This phenomenon can greatly reduce metal oxidation and improve electrolysis efficiency.

[0076] The main technology disclosed herein utilizes electrolytic electrode design in a fluorine-containing molten salt metal electrolysis system to improve the electrolytic metal recovery rate and reduce the anode current density, thereby preventing the decomposition of the fluoride salt electrolyte to produce fluorine gas / fluoride, thereby depositing and concentrating rare earth metals and increasing metal yield.

[0077] The above embodiments are provided so that those skilled in the art can better understand the concepts of the embodiments of the present invention. Those skilled in the art should understand that they can design or modify other processes and components based on the embodiments of the present invention to achieve the same objectives and / or advantages as the embodiments described herein. Those skilled in the art should also understand that such similar processes and components do not depart from the spirit and scope of the present invention, and that they can make various changes, substitutions, and replacements without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the scope of the appended claims. Furthermore, although the present invention has been disclosed above with reference to several preferred embodiments, these are not intended to limit the present invention.

[0078] Reference throughout this specification to features, advantages, or similar language does not imply that all features and advantages that may be realized with the present invention should or may be realized in any single embodiment of the present invention. Rather, language referring to features and advantages is understood to mean that a specific feature, advantage, or characteristic described in connection with an embodiment is included in at least one embodiment of the present invention. Thus, discussion of features and advantages, and similar language, throughout this specification may, but do not necessarily, refer to the same embodiment.

[0079] Furthermore, the described features, advantages, and characteristics of the present invention may be combined in any suitable manner in one or more embodiments. Based on the description herein, one skilled in the relevant art will recognize that the present invention may be practiced without one or more of the specific features or advantages of a particular embodiment. In other cases, additional features and advantages may be identified in certain embodiments that may not be present in all embodiments of the present invention.

[0080] 10: Electrolysis system 12: cathode 12 B: bottom of cathode 12 Bb: top of the bottom of the cathode 14: Anode 12 B', 12 B": the sides of the bottom of the cathode a, b: length of the side of the bottom of the cathode C: cathode diameter γ: angle of the sharp corner

Claims

1. A cathode for rare earth molten salt electrolysis, comprising: A solid cylinder having a conical base and a pointed or flat apex; wherein when the apex of the cone is pointed, the angle of the pointed angle is between 5 degrees and 175 degrees.

2. The cathode for rare earth molten salt electrolysis as described in claim 1, wherein the cathode is composed of tungsten, molybdenum, or tantalum.

3. The cathode for rare earth molten salt electrolysis as described in claim 1, wherein when the lengths of the conical side sides are equal, the angle of the apex is obtained by formula (I): c2=2a2(1-cos(γ)) (I), where c is the diameter of the cylinder, a is the length of the conical side side, and γ is the angle of the apex.

4. The cathode for rare earth molten salt electrolysis as described in claim 1, wherein the lengths of the conical sides are different.

5. An electrolysis system, comprising: A cathode as described in claim 1; At least one anode; And an electrolyte comprising rare earth oxides, wherein the cathode and the at least one anode are disposed in the electrolyte, and wherein the ratio of the surface area of ​​the cathode to the surface area of ​​the at least one anode is between 1:100 and 1:

1.

6. The electrolysis system as claimed in claim 5, wherein when the top of the cone is a sharp angle and the lengths of the sides of the cone are equal, the angle of the sharp angle is obtained by formula (I): c2=2a2(1-cos(γ)) (I), where c is the diameter of the cylinder, a is the length of the side of the cone, and γ is the angle of the sharp angle.

7. The electrolysis system as claimed in claim 5, wherein the top of the cone is a sharp angle and the sides of the cone are of different lengths.

8. The electrolysis system as claimed in claim 5, wherein the at least one anode surrounds the cathode.

9. The electrolysis system as claimed in claim 5, wherein the cathode is composed of tungsten, molybdenum, or tantalum.

10. The electrolysis system as claimed in claim 5, wherein the at least one anode is composed of graphite.

11. The electrolysis system as claimed in claim 5, wherein the rare earth oxide includes neodymium oxide, tungsten oxide or dysprosium oxide.

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