Gradation evaluation and particle size control method for high-purity quartz slurry
By measuring and adjusting the particle size distribution coefficient of quartz sand particles, the problems of unreasonable particle grading and uneven particle size distribution in the preparation of quartz slurry are solved, and the stability and controllability of high-purity quartz slurry are achieved, improving the stability and controllability of high-purity quartz slurry Product quality.
Patent Information
- Application Number
- CN202411517841.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-29
- Publication Date
- 2024-12-27
AI Technical Summary
During the preparation process of existing quartz slurry, there are problems such as unreasonable particle grading and uneven particle size distribution, resulting in unstable slurry performance and affecting product quality and production efficiency.
By measuring the equivalent particle size of quartz sand particles, calculating particle size distribution coefficients n1 and n2, adjusting particle size, ensuring that the values of D10, D50, and D90 meet the standards, and then controlling the grading and particle size distribution of high-purity quartz slurry, improving Flowability, fillability and uniformity of the slurry.
Grading evaluation and particle size control of high-purity quartz slurry are realized, ensuring the stability and controllability of the preparation process, and improving the slurry performance and product quality.
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Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of high-purity quartz sand slurry preparation, and in particular to a high-purity quartz slurry gradation evaluation and particle size control method. Background Art
[0002] High-purity quartz sand mortar is a mortar material formed by fine processing of high-purity quartz particles, with uniform particle size distribution and excellent physical and chemical properties. It is widely used in high-tech fields such as high-end optics, semiconductors, photovoltaics and microelectronics. Its performance directly affects the quality and application effect of the product. The performance of quartz slurry is closely related to its particle grading and particle size distribution. Reasonable particle grading and particle size distribution can improve the fluidity, filling and uniformity of the slurry, thereby preparing high-quality quartz products. However, in the existing quartz slurry preparation process, there are often problems such as unreasonable particle grading and uneven particle size distribution, which leads to unstable slurry performance and affects product quality and production efficiency. Therefore, those skilled in the art provide a method for evaluating the grading of high-purity quartz slurry and controlling particle size to solve the problems raised in the above background technology. Summary of the invention
[0003] The object of the present invention is to provide a method for evaluating the grading of high-purity quartz slurry and controlling the particle size to solve the problems raised in the above-mentioned background technology.
[0004] To achieve the above object, the present invention provides the following technical solutions:
[0005] A method for evaluating the gradation of high-purity quartz slurry and controlling the particle size, the method comprising the following steps:
[0006] Step 1: Select high-purity quartz raw materials, and use quartz sand particle preparation equipment to crush, screen, and remove dust from the high-purity quartz raw materials to remove impurities and fine powder in the high-purity quartz raw materials to obtain quartz sand particles;
[0007] Step 2: Measure the equivalent particle size of the quartz sand particles obtained in step 1 to obtain the particle size D of the quartz sand particles. 10 , D 50 , D 90 value;
[0008] Step 3: According to the particle size D of the quartz sand obtained in step 2 10 , D 50 , D 90 Calculate the particle size distribution coefficient n1 of the quartz sand particles, and confirm whether the quartz sand particle grading is reasonable based on the calculated value of n1. If it is unreasonable, adjust the D 10 , D 50 , D 90 The particle size distribution coefficient n1 is calculated as follows:
[0009]
[0010] Where n1 is the particle size distribution coefficient, CPFT is the cumulative percentage below a certain particle size D, D is the particle size corresponding to CPFT, and D L is the maximum particle size.
[0011] Step 4: According to the particle size D of the quartz sand obtained in step 2 10 , D 50 , D 90 The particle size distribution coefficient n2 of the quartz sand particles is calculated, and the particle size of the quartz sand particles is confirmed to meet the requirements according to the calculated value of n2. If it does not meet the requirements, the parameters of the quartz sand particle preparation equipment are adjusted and the quartz sand particles are re-prepared. The calculation formula of the particle size distribution coefficient n2 is as follows:
[0012]
[0013] Where n2 is the particle size distribution coefficient, CPFT is the cumulative percentage below a certain particle size D, D is the particle size corresponding to CPFT, and D S is the minimum particle size, D L is the maximum particle size;
[0014] Step 5: grinding the quartz sand particles, and mixing the ground quartz sand particles with pure water to obtain high-purity quartz slurry;
[0015] Step 6: Test the fluidity, viscosity, filling and uniformity of the high-purity quartz slurry obtained in step 5, confirm that the fluidity, viscosity, filling and uniformity of the high-purity quartz slurry meet the standards, and complete the particle grading and particle size control of the high-purity quartz slurry.
[0016] Preferably, the purity of the high-purity quartz raw material provided in step 1 is not less than 99.99%.
[0017] Preferably, the device for measuring the equivalent particle size of the quartz sand particles in step 2 is a laser particle size analyzer.
[0018] Preferably, the equivalent particle size proposed in step 2 is the maximum distance between tangent lines in the short axis direction of the quartz sand particles.
[0019] Preferably, the quartz sand particle size D proposed in step 2 is 10 , D 50 , D 90 The values are the particle diameters corresponding to 10%, 50%, and 90% of the total particles on the cumulative distribution curve, and the D 50 is the median particle size.
[0020] Preferably, the quartz sand particle size D proposed in step 3 is 10 , D 50 , D 90 The calculation method of substituting the value into formula (1) is as follows:
[0021] D 50 Substitute the value into formula (1) to obtain formula (1-1), as follows:
[0022]
[0023] D 90 Substitute the value into formula (1) to obtain formula (1-2), as follows:
[0024]
[0025] Dividing formula (1-1) by formula (1-2) yields formula (1-3), as follows:
[0026]
[0027] Taking the logarithm of both sides of formula (1-3), we get formula (1-4), as follows:
[0028]
[0029] Where n1 is the particle size distribution coefficient, D L is the maximum particle size.
[0030] Preferably, the particle size distribution coefficient n1 of the quartz sand particles proposed in step three has a numerical range of 0.33-0.5.
[0031] Preferably, the quartz sand particle size D proposed in step 4 is 10 , D 50 , D 90 The calculation method of substituting the value into formula (2) is as follows:
[0032] D 10 Substitute the value into formula (2) to obtain formula (2-1), as follows:
[0033]
[0034] D 50 Substitute the value into formula (2) to obtain formula (2-2), as follows:
[0035]
[0036] D 90 Substitute the value into formula (2) to obtain formula (2-3), as follows:
[0037]
[0038] Subtracting formula (2-3) from formula (2-2) yields formula (2-4), as follows:
[0039]
[0040] Subtracting formula (2-2) from formula (2-3) yields formula (2-5), as follows:
[0041]
[0042] Divide formula (2-5) by formula (2-4) to obtain formula (2-6), as follows:
[0043]
[0044] Where n2 is the particle size distribution coefficient, D S is the minimum particle size, D L is the maximum particle size.
[0045] Preferably, the particle size distribution coefficient n2 value of the quartz sand particles proposed in step 4 is ≤0.37.
[0046] Preferably, the equipment for preparing quartz sand particles proposed in step 1 and step 4 is a grinding machine and a screen.
[0047] Compared with the prior art, the advantages of the present invention are as follows: the high-purity quartz slurry grading evaluation and particle size control method proposed in the present invention first measures the equivalent particle size of the quartz sand particles to obtain the D 10 , D 50 , D 90 value, and according to the particle size D of the quartz sand 10 , D 50 , D 90 The particle size distribution coefficient n1 value is calculated based on the value of n1, and whether the n1 value meets the standard is determined to judge whether the gradation of high-purity quartz slurry is reasonable. 10 , D 50 , D 90 The particle size distribution coefficient n2 value is calculated according to D 10 and D 50 Value, D 10 and D 90 Calculate D for different n2 values 90 Value, D 50 value, get D 90 Value, D 50The control range of the value is controlled, and the particle size of the high-purity quartz slurry grading particles is controlled. Finally, high-purity quartz slurry is made according to the reasonable quartz particle size grading, and the performance of the high-purity quartz slurry is tested to confirm that the performance of the high-purity quartz slurry meets the standard. In this way, the grading evaluation and particle size control of the high-purity quartz slurry are realized, and the grading evaluation of the quartz sand particles can be accurately measured and evaluated, the preparation process of the quartz sand particles can be adjusted, the particle size of the quartz sand particles can be controlled, the stability and controllability of the high-purity quartz sand slurry preparation process can be ensured, and the performance of the slurry and the product quality can be improved. BRIEF DESCRIPTION OF THE DRAWINGS
[0048] Figure 1 This is a flowchart of high-purity quartz slurry grading evaluation and particle size control according to an embodiment of the present invention;
[0049] Figure 2 FIG. 4 is a schematic diagram of particle size distribution of high-purity quartz slurry according to an embodiment of the present invention. DETAILED DESCRIPTION
[0050] In the description of the present invention, it should be understood that the terms "center", "lateral", "up", "down", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, which are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first" and "second" are used only for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more. In addition, the term "including" and any variation thereof are intended to cover non-exclusive inclusions.
[0051] Overall implementation scheme:
[0052] Combination Figure 1 and Figure 2 As shown, a method for evaluating the gradation of high-purity quartz slurry and controlling the particle size comprises the following steps: step 1, selecting a high-purity quartz raw material, and using a quartz sand particle preparation device to crush, screen, and dust the high-purity quartz raw material to remove impurities and fine powder in the high-purity quartz raw material to obtain quartz sand particles; step 2, measuring the equivalent particle size of the quartz sand particles obtained in step 1 to obtain the particle size D of the quartz sand particles. 10 , D 50 , D 90Step 3: According to the quartz sand particle size D obtained in step 2 10 , D 50 , D 90 Calculate the particle size distribution coefficient n1 of the quartz sand particles, and confirm whether the quartz sand particle grading is reasonable based on the calculated value of n1. If it is unreasonable, adjust the D 10 , D 50 , D 90 Step 4: according to the particle size of the quartz sand particles obtained in step 2, D 10 , D 50 , D 90 The particle size distribution coefficient n2 of the quartz sand particles is calculated according to the value of n2, and whether the particle size of the quartz sand particles meets the requirements is confirmed according to the calculated value of n2. If it does not meet the requirements, the parameters of the quartz sand particle preparation equipment are adjusted to re-prepare the quartz sand particles; Step five, grind the quartz sand particles, and mix the ground quartz sand particles with pure water to obtain high-purity quartz slurry; Step six, test the fluidity, viscosity, filling and uniformity of the high-purity quartz slurry obtained in Step five, confirm that the fluidity, viscosity, filling and uniformity of the high-purity quartz slurry meet the standards, and complete the particle grading and particle size control of the high-purity quartz slurry.
[0053] The calculation formula for the particle size distribution coefficient n1 proposed in step 3 is as follows:
[0054]
[0055] D 50 Substitute the value into formula (1) to obtain formula (1-1), as follows:
[0056]
[0057] D 90 Substitute the value into formula (1) to obtain formula (1-2), as follows:
[0058]
[0059] Dividing formula (1-1) by formula (1-2) yields formula (1-3), as follows:
[0060]
[0061] Taking the logarithm of both sides of formula (1-3), we get formula (1-4), as follows:
[0062]
[0063] Where n1 is the particle size distribution coefficient, CPFT is the cumulative percentage below a certain particle size D, D is the particle size corresponding to CPFT, and D Lis the maximum particle size.
[0064] The calculation formula for the particle size distribution coefficient n2 proposed in step 4 is as follows:
[0065]
[0066] D 10 Substitute the value into formula (2) to obtain formula (2-1), as follows:
[0067]
[0068] D 50 Substitute the value into formula (2) to obtain formula (2-2), as follows:
[0069]
[0070] D 90 Substitute the value into formula (2) to obtain formula (2-3), as follows:
[0071]
[0072] Subtracting formula (2-3) from formula (2-2) yields formula (2-4), as follows:
[0073]
[0074] Subtracting formula (2-2) from formula (2-3) yields formula (2-5), as follows:
[0075]
[0076] Divide formula (2-5) by formula (2-4) to obtain formula (2-6), as follows:
[0077]
[0078] Where n2 is the particle size distribution coefficient, CPFT is the cumulative percentage below a certain particle size D, D is the particle size corresponding to CPFT, and D S is the minimum particle size, D L is the maximum particle size.
[0079] Example 1
[0080] The method for evaluating the particle grading of high-purity quartz is as follows:
[0081] (1) selecting a high-purity quartz raw material with a purity of not less than 99.99%, crushing the high-purity quartz raw material with a grinding machine, crushing the high-purity quartz raw material into fine particles, and filtering out fine powder and larger particles in the quartz raw material with a sieve to obtain quartz sand particles;
[0082] (2) Use a laser particle size analyzer to measure the equivalent particle size of quartz sand particles, and obtain the particle diameter D corresponding to 10%, 50%, and 90% of the total particles on the quartz sand particle size distribution curve. 10 , D 50 , D 90 value;
[0083] (3) The particle size of the quartz sand is D 10 , D 50 , D 90 Substitute the value into formula (1) to calculate the value of the particle size distribution coefficient n1 of the quartz sand particles, and confirm whether the value of n1 meets the range standard. If it is unreasonable, adjust the D 10 , D 50 , D 90 The particle size of the quartz sand is recalculated, and the value of the particle size distribution coefficient n1 is recalculated;
[0084] (4) The particle size of the quartz sand is D 10 , D 50 , D 90 Substitute the value into formula (2) to calculate the value of the particle size distribution coefficient n2 of the quartz sand particles, and confirm whether the value of n2 meets the range standard. If it does not meet the requirements, adjust the grinding mill parameters, change the crushing time of the high-purity quartz sand raw material, replace the sieves with different mesh sizes, re-prepare the quartz sand particles, and measure and repeat the above steps (1), (2), and (3) to recalculate the value of the particle size distribution coefficient n2 of the quartz sand particles;
[0085] (5) grinding the quartz sand particles with a grinding machine, and mixing the ground quartz sand particles with pure water with a mixer to obtain a high-purity quartz slurry;
[0086] (6) Test the fluidity, viscosity, filling and uniformity of the high-purity quartz slurry obtained in step 5 to confirm that the fluidity, viscosity, filling and uniformity of the high-purity quartz slurry meet the standards, and complete the particle grading and particle size control of the high-purity quartz slurry.
[0087] The following is the calculation of the particle size distribution coefficient n1 value and n2 value for different particle size values:
[0088]
[0089]
[0090] Embodiment 2:
[0091] The calculation method of high purity quartz sand particle size is as follows:
[0092] (1) selecting a high-purity quartz raw material with a purity of not less than 99.99%, crushing the high-purity quartz raw material with a grinding machine, crushing the high-purity quartz raw material into fine particles, and filtering out fine powder and larger particles in the quartz raw material with a sieve to obtain quartz sand particles;
[0093] (2) Use a laser particle size analyzer to measure the equivalent particle size of quartz sand particles, and obtain the particle diameter D corresponding to 10%, 50%, and 90% of the total particles on the quartz sand particle size distribution curve. 10 , D 50 , D 90 value;
[0094] (3) According to the n1 value, the particle size D of the quartz sand particles 10 , D 90 Substitute the value into formula (1-4) to calculate the quartz sand particle D 50 The value of quartz sand particles D 50 Is the value within the standard range? If not, adjust the quartz sand particles D 50 The particle size of quartz sand can be controlled to achieve the grading evaluation and particle size control of quartz sand particles;
[0095] (4) According to the n2 value, the particle size D of the quartz sand particles 10 , D 90 Substitute the value into formula (2-6) to calculate the quartz sand particle D 50 The value of quartz sand particles D 50 Is the value within the standard range? If not, change the crushing time of the high-purity quartz sand raw material, replace the sieve with different mesh sizes, re-prepare the quartz sand particles, and make the quartz sand particles D 50 The value is within the standard range, realizing the grading evaluation and particle size control of quartz sand particles.
[0096] According to the value of n1 and n2, D 10 Value, D 90 Substitute the value into formula (1-4) and (2-6) to calculate D 50 The value range is shown in the following table:
[0097]
[0098]
[0099]
[0100] Example 3
[0101] The calculation method of high purity quartz sand particle size is as follows:
[0102] (1) selecting a high-purity quartz raw material with a purity of not less than 99.99%, crushing the high-purity quartz raw material with a grinding machine, crushing the high-purity quartz raw material into fine particles, and filtering out fine powder and larger particles in the quartz raw material with a sieve to obtain quartz sand particles;
[0103] (2) Use a laser particle size analyzer to measure the equivalent particle size of quartz sand particles, and obtain the particle diameter D corresponding to 10%, 50%, and 90% of the total particles on the quartz sand particle size distribution curve. 10 , D 50 , D 90 value;
[0104] (3) According to the n1 value, the particle size D of the quartz sand particles 10 , D 50 Substitute the value into formula (1-4) to calculate the quartz sand particle D 90 The value of quartz sand particles D 90 Is the value within the standard range? If not, adjust the quartz sand particles D 90 The particle size of quartz sand can be controlled to achieve the grading evaluation and particle size control of quartz sand particles;
[0105] (4) According to the n2 value, the particle size D of the quartz sand particles 10 , D 50 Substitute the value into formula (2-6) to calculate the quartz sand particle D 90 The value of quartz sand particles D 90 Is the value within the standard range? If not, change the crushing time of the high-purity quartz sand raw material, replace the sieve with different mesh sizes, re-prepare the quartz sand particles, and make the quartz sand particles D 90 The value is within the standard range, realizing the grading evaluation and particle size control of quartz sand particles.
[0106]
[0107]
[0108] The working principle of the present invention is as follows: the high-purity quartz slurry grading evaluation and particle size control method proposed in the present application first measures the equivalent particle size of the quartz sand particles to obtain the D 10 , D 50 , D 90 value, and according to the particle size D of the quartz sand 10 , D 50 , D 90 The particle size distribution coefficient n1 value is calculated based on the value of n1, and whether the n1 value meets the standard is determined to judge whether the gradation of high-purity quartz slurry is reasonable. 10 , D 50 , D90 The particle size distribution coefficient n2 value is calculated according to D 10 and D 50 Value, D 10 and D 90 Calculate D for different n2 values 90 Value, D 50 value, get D 90 Value, D 50 The control range of the value is controlled, and the particle size of the high-purity quartz slurry grading particles is controlled. Finally, high-purity quartz slurry is made according to the reasonable quartz particle size grading, and the performance of the high-purity quartz slurry is tested to confirm that the performance of the high-purity quartz slurry meets the standard. In this way, the grading evaluation and particle size control of the high-purity quartz slurry are realized, and the grading evaluation of the quartz sand particles can be accurately measured and evaluated, the preparation process of the quartz sand particles can be adjusted, the particle size of the quartz sand particles can be controlled, the stability and controllability of the high-purity quartz sand slurry preparation process can be ensured, and the performance of the slurry and the product quality can be improved.
[0109] What is described above is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.
Claims
1. A method for evaluating the gradation of high-purity quartz slurry and controlling the particle size, characterized in that: The method comprises the following steps: Step 1: Select high-purity quartz raw materials, and use quartz sand particle preparation equipment to crush, screen, and remove dust from the high-purity quartz raw materials to remove impurities and fine powder in the high-purity quartz raw materials to obtain quartz sand particles; Step 2: Measure the equivalent particle size of the quartz sand particles obtained in step 1 to obtain the particle size D of the quartz sand particles. 10 , D 50 , D 90 value; Step 3: According to the particle size D of the quartz sand obtained in step 2 10 , D 50 , D 90 Calculate the particle size distribution coefficient n1 of the quartz sand particles, and confirm whether the quartz sand particle grading is reasonable based on the calculated value of n1. If it is unreasonable, adjust the D 10 , D 50 , D 90 The particle size distribution coefficient n1 is calculated as follows: Where n1 is the particle size distribution coefficient, CPFT is the cumulative percentage below a certain particle size D, D is the particle size corresponding to CPFT, and D L is the maximum particle size. Step 4: According to the particle size D of the quartz sand obtained in step 2 10 , D 50 , D 90 The particle size distribution coefficient n2 of the quartz sand particles is calculated, and the particle size of the quartz sand particles is confirmed to meet the requirements according to the calculated value of n2. If it does not meet the requirements, the parameters of the quartz sand particle preparation equipment are adjusted and the quartz sand particles are re-prepared. The calculation formula of the particle size distribution coefficient n2 is as follows: Where n2 is the particle size distribution coefficient, CPFT is the cumulative percentage below a certain particle size D, D is the particle size corresponding to CPFT, and D S is the minimum particle size, D L is the maximum particle size; Step 5: grinding the quartz sand particles, and mixing the ground quartz sand particles with pure water to obtain high-purity quartz slurry; Step 6: Test the fluidity, viscosity, filling and uniformity of the high-purity quartz slurry obtained in step 5, confirm that the fluidity, viscosity, filling and uniformity of the high-purity quartz slurry meet the standards, and complete the particle grading and particle size control of the high-purity quartz slurry.
2. A method for evaluating grading and controlling particle size of high-purity quartz slurry according to claim 1, characterized in that: The purity of the high-purity quartz raw material provided in step 1 is not less than 99.99%.
3. A method for evaluating grading and controlling particle size of high-purity quartz slurry according to claim 1, characterized in that: The device for measuring the equivalent particle size of the quartz sand particles in the step 2 is a laser particle size analyzer.
4. A method for evaluating grading and controlling particle size of high-purity quartz slurry according to claim 1, characterized in that: The equivalent particle size proposed in the step 2 is the maximum distance between tangent lines in the short axis direction of the quartz sand particles.
5. A method for evaluating grading and controlling particle size of high-purity quartz slurry according to claim 1, characterized in that: The particle size D of the quartz sand particles proposed in step 2 10 , D 50 , D 90 The values are the particle diameters corresponding to 10%, 50%, and 90% of the total particles on the cumulative distribution curve, and the D 50 is the median particle size.
6. A method for evaluating grading and controlling particle size of high-purity quartz slurry according to claim 1, characterized in that: The particle size D of the quartz sand particles proposed in step 3 10 , D 50 , D 90 The calculation method of substituting the value into formula (1) is as follows: D 50 Substitute the value into formula (1) to obtain formula (1-1), as follows: D 90 Substitute the value into formula (1) to obtain formula (1-2), as follows: Dividing formula (1-1) by formula (1-2) yields formula (1-3), as follows: Taking the logarithm of both sides of formula (1-3), we get formula (1-4), as follows: Where n1 is the particle size distribution coefficient, D L is the maximum particle size.
7. A method for evaluating gradation and controlling particle size of high-purity quartz slurry according to claim 1, characterized in that: The numerical range of the particle size distribution coefficient n1 of the quartz sand particles proposed in the step 3 is 0.33-0.
5.
8. A method for evaluating grading and controlling particle size of high-purity quartz slurry according to claim 1, characterized in that: The particle size D of the quartz sand particles proposed in step 4 is 10 , D 50 , D 90 The calculation method of substituting the value into formula (2) is as follows: D 10 Substitute the value into formula (2) to obtain formula (2-1), as follows: D 50 Substitute the value into formula (2) to obtain formula (2-2), as follows: D 90 Substitute the value into formula (2) to obtain formula (2-3), as follows: Subtracting formula (2-3) from formula (2-2) yields formula (2-4), as follows: Subtracting formula (2-2) from formula (2-3) yields formula (2-5), as follows: Divide formula (2-5) by formula (2-4) to obtain formula (2-6), as follows: Where n2 is the particle size distribution coefficient, D S is the minimum particle size, D L is the maximum particle size.
9. A method for evaluating grading and controlling particle size of high-purity quartz slurry according to claim 1, characterized in that: The particle size distribution coefficient n2 value of the quartz sand particles proposed in the step 4 is ≤0.
37.
10. A method for evaluating grading and controlling particle size of high-purity quartz slurry according to claim 1, characterized in that: The equipment for preparing quartz sand particles proposed in step 1 and step 4 is a grinding machine and a screen.
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