Alkali-sulfate composite activator for solid waste cementing material and preparation method of alkali-sulfate composite activator

The synergistic effect of the three components of the alkali-sulfate composite activator has solved the problems of slow hydration rate and low early strength of industrial solid waste cementitious materials, realizing the compatibility and performance improvement of various solid wastes, and promoting the high-value utilization and environmental benefits of industrial solid waste.

CN121758093APending Publication Date: 2026-03-31GUANGXI UNIVERSITY OF TECHNOLOGY +1
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-01-08
Publication Date
2026-03-31

AI Technical Summary

Technical Problem

Existing technologies lack a composite activation system that can solve the problems of slow hydration rate, low early strength, and poor carbonization resistance of industrial solid waste cementitious materials through multi-component synergistic and synchronous solutions, and it is difficult to adapt to various industrial solid wastes and be compatible with trace impurities.

Method used

An alkali-sulfate composite activator was developed, which consists of three components: sulfate coagulation promoter, alkali densifier, and seed crystal enhancer. By optimizing the component parameters and preparation process, a widely adaptable activator was prepared for use in industrial by-products gypsum and siliceous aluminum solid waste, thereby improving the hydration rate and early strength and optimizing the anti-carbonation performance.

Benefits of technology

It significantly improves the early strength and hydration rate of solid waste cementitious materials, optimizes carbonization resistance and compaction properties, is suitable for various industrial solid wastes, promotes the high-value utilization of industrial solid wastes, reduces carbon emissions, and has broad engineering application value.

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Abstract

The invention discloses an alkali-sulfate composite activator for a solid waste cementing material and a preparation method, the alkali-sulfate composite activator comprises the following raw materials in parts by weight: 33-57 parts of a sulfate coagulation-accelerating excitation component, 27-48 parts of an alkali compact excitation component and 9-21 parts of a seed crystal synergistic component, the sulfate coagulation-accelerating excitation component comprises aluminum sulfate and sodium aluminum sulfate in a mass ratio of (1.5-2.8): 1, and the seed crystal synergistic component comprises sodium sulfate and sodium sulfate in a mass ratio of (1.5-2.8): 1. The alkali compact excitation component comprises sodium sulfate and sodium aluminum sulfate in a mass ratio of (1.0-1.8): 1, and the seed crystal synergist is ettringite seed crystal. According to the invention, by doping the sulfate coagulating excitation component, the alkali compact excitation component and the seed crystal synergistic component, the generation of ettringite can be accelerated to solve the problem of slow hydration, the formation of sodium aluminosilicate gel is promoted to improve the compactness and synchronously improve the hydration efficiency and carbonization resistance, and under the condition that the doping amount is 3.5%-8.5%, the content of the sodium aluminosilicate gel can be increased. According to the method, the 3d compressive strength of the solid waste cementing material can be improved to 19.5 MPa or above, the 28d carbonization depth can be reduced to 4.2 mm or below, the total utilization rate of the solid waste reaches 70% or above, and the method has remarkable environmental protection benefits, economic benefits and engineering application value.
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Description

Technical Field

[0001] This invention relates to the fields of solid waste resource utilization and low-carbon building materials technology, and particularly to an alkali-sulfate composite activator for solid waste cementitious materials and its preparation method. Background Technology

[0002] With the transformation and upgrading of my country's industry, the large-scale disposal and high-value utilization of industrial solid waste has become a core task in the construction of ecological civilization. This involves using industrial by-products such as gypsum (desulfurization gypsum, phosphogypsum, titanium gypsum, etc.) and siliceous aluminous solid waste (granulated blast furnace slag powder, fly ash, steel slag powder, etc.) to prepare green cementitious materials to replace traditional cement. However, due to the inherent defects of solid waste, there are still many technical bottlenecks in practical applications: slow hydration rate, insufficient early strength, poor carbonization resistance, insufficient durability, and limited performance improvement.

[0003] While activators can effectively address the aforementioned technical bottlenecks, existing technologies lack a composite activation system that combines targeted activation, synergistic enhancement, and solid waste compatibility. This system cannot simultaneously solve the core problems of slow hydration rate, low early strength, and poor carbonization resistance through multi-component synergy, nor can it be adapted to various industrial solid waste composite systems, nor can it be compatible with trace impurities in solid waste. Therefore, developing a dual-activation synergistic enhancement composite activator with a clear mechanism, stable performance, and wide compatibility is crucial for promoting the high-value utilization of "industrial by-product gypsum-silica aluminate solid waste." This invention proposes an alkali-sulfate composite activator for solid waste cementitious materials and its preparation method. Through the synergistic effect of sulfate coagulation, alkali densification, and seed crystal enhancement, the component parameters and preparation process are optimized, the activator dosage is controlled, and the preparation process is simplified. This method can adapt to various industrial solid wastes, simultaneously solving the bottleneck problems of slow hydration rate, low early strength, and poor carbonization resistance in solid waste cementitious materials. It also considers engineering application performance and industrial production feasibility, promoting the high-value utilization of solid waste resources. Summary of the Invention

[0004] The purpose of this invention is to provide an alkali-sulfate composite activator for solid waste cementitious materials and its preparation method.

[0005] To achieve the above objectives, the present invention is implemented according to the following technical solution: The alkali-sulfate composite activator for solid waste cementitious materials comprises the following raw materials in the following weight ratios: 33-57 parts of sulfate coagulation activating component, 27-48 parts of alkali densifying activating component, and 9-21 parts of seed crystal enhancing component; the sulfate coagulation activating component comprises aluminum sulfate and sodium aluminum sulfate in a mass ratio of 1.5-2.8:1; the alkali densifying activating component comprises sodium sulfate and sodium aluminum sulfate in a mass ratio of 1.0-1.8:1; the seed crystal enhancing component is ettringite seed crystal; the dosage of the alkali-sulfate composite activator is 3.5%-8.5% of the total dry basis mass of the solid waste cementitious material; the solid waste cementitious material contains industrial by-product gypsum and siliceous aluminum solid waste, wherein industrial by-product gypsum accounts for 30%-70% of the total mass of the cementitious material.

[0006] Furthermore, the particle size distribution of the alkali-sulfate composite activator satisfies the following conditions: 100% passing through a 70μm square hole sieve, median particle size D50 = 8-12μm, and particle size variation coefficient CV ≤ 5%.

[0007] Furthermore, the aluminum sulfate satisfies the following condition: specific surface area ≥ 480 m². 2 / kg, moisture content ≤1.5%, purity ≥98.5%.

[0008] Furthermore, sodium sulfate meets the following requirement: specific surface area ≥ 500 m². 2 / kg, moisture content ≤0.5%, purity ≥99.5% Furthermore, the sodium aluminum sulfate satisfies the following condition: specific surface area ≥ 520 m². 2 / kg, moisture content ≤1.0%, purity ≥96%.

[0009] Furthermore, the ettringite seed crystals satisfy the following condition: specific surface area ≥ 450 m². 2 / kg, median particle size D50≤6μm, intensity ratio of characteristic peak of ettringite at 2θ in X-ray diffraction pattern≥0.8; wherein θ is 4.55°, 7.95°, 10.4°.

[0010] The preparation method of the alkali-sulfate composite activator for solid waste cementitious materials includes the following steps: S1. Raw material pretreatment: Aluminum sulfate, sodium sulfate and sodium aluminum sulfate are dried and ground respectively; S2. Preparation of ettringite seed crystals: Aluminum sulfate, calcium sulfate and sodium hydroxide are dissolved in deionized water at a mass ratio of 3.2:2.1:1. The mixture is first stirred and reacted at 55-65℃ for 2-3 hours, and then heated to 70-75℃ and reacted for another 1.5-3 hours. The pH value at the final reaction point is controlled at 10.5-11.5. The ettringite seed crystals are obtained by filtration, washing, drying and grinding. S3. Dry material homogenization and mixing: First, mix the pretreated aluminum sulfate, sodium sulfate and sodium aluminum sulfate according to the designed mass parts, then add the designed mass parts of ettringite seed crystals, and mix in a mixer at a speed of 300-350 r / min for 35-50 minutes until the coefficient of variation of the mixing uniformity is ≤3%, and package under inert gas protection.

[0011] Furthermore, in the preparation of the ettringite seed crystals, the conductivity of the washing liquid of the washed filter cake is ≤20μS / cm.

[0012] The beneficial effects of this invention are: This invention relates to an alkali-sulfate composite activator for solid waste cementitious materials and its preparation method. Compared with the prior art, this invention has the following technical advantages: The composite activator of this invention, through the synergistic effect of its three components, significantly improves the early strength and hydration rate of solid waste cementitious materials, greatly optimizes their resistance to carbonization and compaction properties, and enhances their volume stability. This invention, through component optimization and impurity suppression mechanisms, can be efficiently adapted to various industrial by-product gypsum and is compatible with multiple types of siliceous aluminous solid wastes, breaking the limitation of existing activators that are "suitable for a single solid waste". This invention promotes the high-value utilization of industrial solid waste, and has both environmental and resource benefits, such as high solid waste utilization rate, significant reduction in carbon emissions, and wide range of engineering applications. The solid waste cementitious material prepared by the composite activator of this invention meets stringent engineering requirements in terms of long-term performance and durability. In summary, the composite activator of this invention has a clear mechanism, excellent performance, controllable cost, and wide applicability, providing an efficient solution for the high-value utilization of industrial by-products gypsum and silica-alumina solid waste, and has important engineering application value, environmental value, and economic value. Attached Figure Description

[0013] Figure 1 This is a flowchart illustrating the preparation method of the alkali-sulfate composite activator for solid waste cementitious materials according to the present invention. Figure 2 The X-ray diffraction pattern of ettringite seed crystals in the alkali-sulfate composite activator of this invention; Figure 3 This is a particle size distribution diagram of the alkali-sulfate composite activator of the present invention; Figure 4 This is a scanning electron microscope image of the hydration products under the action of the alkali-sulfate composite activator of the present invention; Figure 5 This is a comparison diagram of the material properties of solid waste cementitious materials using different activators according to the present invention; Figure 6 This is a comparison chart of the material properties of solid waste cementitious materials using different dosages of alkali-sulfate composite activators according to the present invention. Detailed Implementation

[0014] The present invention will be further described below through specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0015] The present invention relates to a method for preparing an alkali-sulfate composite activator for solid waste cementitious materials, comprising the following steps: like Figure 1 As shown, this embodiment includes the following steps: S1. Raw material pretreatment: Aluminum sulfate, sodium sulfate and sodium aluminum sulfate are dried and ground respectively; S2. Preparation of ettringite seed crystals: Aluminum sulfate, calcium sulfate and sodium hydroxide are dissolved in deionized water at a mass ratio of 3.2:2.1:1. The mixture is first stirred and reacted at 55-65℃ for 2-3 hours, and then heated to 70-75℃ and reacted for another 1.5-3 hours. The pH value at the final reaction point is controlled at 10.5-11.5. The ettringite seed crystals are obtained by filtration, washing, drying and grinding. S3. Dry material homogenization and mixing: First, mix the pretreated aluminum sulfate, sodium sulfate and sodium aluminum sulfate according to the designed mass parts, then add the designed mass parts of ettringite seed crystals, and mix in a mixer at a speed of 300-350r / min for 35-50 minutes until the coefficient of variation of the mixing uniformity is ≤3%, and package under inert gas protection. In actual preparation, the following raw materials were selected: (1) Industrial by-product gypsum: desulfurized gypsum (a power plant in Shandong, which becomes β-hemihydrate gypsum after calcination), phosphogypsum (a phosphate plant in Yunnan, which is neutralized with lime to pH 6.5-7.5 and then calcined), and titanium gypsum (a titanium dioxide plant in Sichuan, which is calcined after magnetic separation to remove impurities), all of which were dried to a moisture content of ≤1.0%; (2) Silica-alumina solid waste: S95 grade slag powder (a steel plant in Beijing, with a specific surface area of ​​450 m²). 2 / kg), Grade II fly ash (a power plant in Hebei, loss on ignition 6.5%), steel slag powder (a steel plant in Shanghai, aged for 3 months, 28d activity index 96%), dried to moisture content ≤1.0%; (3) aluminum sulfate (calculated as Al2(SO4)3·18H2O): industrial grade, purity ≥98.5%; (4) sodium sulfate (calculated as Na2SO4): industrial grade, purity ≥99.5%; (5) sodium aluminum sulfate (calculated as NaAl(SO4)2): industrial grade, purity ≥96%; (6) calcium sulfate (calculated as CaSO4): analytical grade; (7) sodium hydroxide (calculated as NaOH): industrial grade, purity ≥98%; (8) deionized water: conductivity ≤5μS / cm; After drying and grinding, aluminum sulfate, sodium sulfate, and sodium aluminum sulfate are ensured that the specific surface area and moisture content of the corresponding raw materials meet the usage requirements. The specific drying and grinding operations are as follows: aluminum sulfate is dried at 80-90℃ for 4 hours and then ground using a vibratory mill; sodium sulfate is dried at 105-110℃ for 2 hours and then ground using a ball mill; sodium aluminum sulfate is vacuum dried at 120-130℃ for 3 hours and then ground using an air jet mill. The specific surface area of ​​aluminum sulfate, sodium sulfate, and sodium aluminum sulfate is 490 m². 2 / kg, 510m 2 / kg, 530m 2 / kg, with moisture contents of 1.2%, 0.4%, and 0.8%, respectively; Aluminum sulfate, calcium sulfate, and sodium hydroxide were dissolved in deionized water at a mass ratio of 3.2:2.1:1 and stirred until completely dissolved. The solution was then transferred to a reaction vessel and stirred at 55-65℃ and 300 rpm for 2.5 h. The temperature was then raised to 70-75℃ and the reaction continued for another 2 h (total reaction time 4.5 h). 0.1 mol / L sodium hydroxide was added dropwise to maintain the pH at 10.5-11.5. After cooling to room temperature, the mixture was filtered using a plate and frame filter press. The filter cake was washed four times with deionized water (washing liquid conductivity 18 μS / cm), vacuum dried at 65-70℃ for 15 h, and then ground in a planetary ball mill for 35 min. The powder was then passed through a 325-mesh sieve to obtain ettringite seed crystals. The specific surface area of ​​the ettringite seed crystals was 460 m². 2 / kg, median particle size D50 = 5.2 μm, intensity ratio of ettringite characteristic peak at 2θ in X-ray diffraction pattern 0.85; among which, Figure 2 X-ray diffraction pattern of ettringite seed crystals; According to the designed mass fractions, the pretreated aluminum sulfate, sodium sulfate and sodium aluminum sulfate were put into a three-dimensional motion mixer and premixed at 320 r / min for 18 min. Then, ettringite seed crystals were added and the speed was adjusted to 330 r / min and mixed for 40 min (Al element content variation coefficient 2.6%) to obtain the alkali-sulfate composite activator, which was then packaged with nitrogen (purity ≥99.9%) for protection. The obtained alkali activator raw material passed through a 70μm square-hole sieve with a median particle size D50 of 10.2μm, a particle size variation coefficient CV of 4.2%, and a moisture content of 0.8%. Figure 3 The particle size distribution diagram is shown for the alkali-sulfate composite activator. Figure 4 The image shows the scanning electron microscope (SEM) image of the hydration products under the action of the alkali-sulfate composite activator. As can be seen from the image, the particle size of the activator is slightly smaller than that of the raw materials such as mineral powder (20 μm), and it can improve the strength through the filling and compaction effect.

[0016] In addition, a method for applying an alkali-sulfate composite activator is provided, which uses industrial by-product gypsum (30%-70% of total mass), siliceous aluminate solid waste (slag powder, fly ash, steel slag powder, etc.), and auxiliary admixtures (0-12% of total mass, metakaolin or slag powder, with a specific surface area ≥500 m²). 2 For solid waste cementitious materials composed of ( / kg), add an alkali-sulfate composite activator (dosage is 3.5%-8.5% of the total dry basis mass of the solid waste cementitious materials), dry mix for 2-3 minutes, then add water at a water-cement ratio of 0.35-0.45 and stir for 5-8 minutes to ensure that the fluidity of the freshly mixed slurry is ≥180mm (tested according to GB / T 2419-2005).

[0017] Meanwhile, based on the raw materials and ettringite seed crystals obtained from the above pretreatment, and combined with the composition of solid waste cementitious materials, this invention provides Examples 1-3, which respectively represent three groups of alkali-sulfate composite activator formulations and applicable solid waste cementitious materials and dosages.

[0018] Example 1: Alkali-sulfate composite activator A formulation (for solid waste cementitious materials in desulfurized gypsum-slag powder system): 34 parts aluminum sulfate, 23 parts sodium sulfate, 28 parts sodium aluminum sulfate, and 15 parts ettringite seed crystals; desulfurized gypsum and slag powder each account for 50% of the total dry weight of the solid waste cementitious material, the dosage of alkali-sulfate composite activator A is 5.0% of the total dry weight of the solid waste cementitious material, the water-cement ratio is 0.4, and standard curing is performed; In this embodiment, the alkali-sulfate composite activator and the contrast activator are prepared and applied according to the above method, and the particle size distribution meets the above requirements.

[0019] Example 2: Alkali-sulfate composite activator B formulation (for solid waste cementitious materials in phosphogypsum-fly ash system): 29 parts aluminum sulfate, 19 parts sodium sulfate, 32 parts sodium aluminum sulfate, and 20 parts ettringite seed crystals; phosphogypsum and fly ash account for 60% and 40% of the total dry weight of the solid waste cementitious material, respectively; the dosage of alkali-sulfate composite activator B is 6.5% of the total dry weight of the solid waste cementitious material; the water-cement ratio is 0.4; standard curing is performed. In this embodiment, the alkali-sulfate composite activator and the contrast activator are prepared and applied according to the above method, and the particle size distribution meets the above requirements.

[0020] Example 3: Alkali-sulfate composite activator C formulation (for solid waste cementitious materials in titanium gypsum-steel slag powder system): 33 parts aluminum sulfate, 23 parts sodium sulfate, 26 parts sodium aluminum sulfate, and 18 parts ettringite seed crystals; titanium gypsum and steel slag powder each account for 50% of the total dry weight of the solid waste cementitious material, the dosage of alkali-sulfate composite activator C is 8.5% of the total dry weight of the solid waste cementitious material, the water-cement ratio is 0.4, and standard curing is performed; In this embodiment, the alkali-sulfate composite activator and the contrast activator are prepared and applied according to the above method, and the particle size distribution meets the above requirements.

[0021] In addition, this invention also provides four sets of comparative activator formulations and applicable solid waste cementitious materials and dosages: The formula for a single sulfate comparative activator is as follows: the mass ratio of aluminum sulfate to sodium aluminum sulfate is 2:1; the desulfurized gypsum and slag powder each account for 50% of the total dry weight of the solid waste cementitious material; the dosage of the single sulfate comparative activator is 8% of the total dry weight of the solid waste cementitious material; the water-cement ratio is 0.4; and standard curing is performed. The formula for a single alkali-based activator is as follows: the mass ratio of sodium sulfate to sodium hydroxide is 3:1; in the solid waste cementitious material, desulfurized gypsum and slag powder each account for 50% of the total dry weight; the dosage of the single alkali-based activator is 8% of the total dry weight of the solid waste cementitious material; the water-cement ratio is 0.4; and standard curing is performed. Composite contrast activator formulation: Commercially available X brand solid waste cementitious material activator; desulfurized gypsum and slag powder each account for 50% of the total dry weight of the solid waste cementitious material, the dosage of composite contrast activator is 8% of the total dry weight of the solid waste cementitious material, water-cement ratio is 0.4, standard curing; Blank comparison activator formulation: No activator, in which desulfurized gypsum and slag powder each account for 50% of the total dry basis mass of the corresponding solid waste cementitious material; In this embodiment, the alkali-sulfate composite activator and the contrast activator are prepared and applied according to the above method, and the particle size distribution meets the above requirements.

[0022] The material properties of solid waste cementitious materials using each group of activators were measured as follows: Figure 5 As can be seen from the comparison, the early strength and anti-carbonation performance of the embodiments of the present invention are significantly better than those of the prior art. By using the alkali-sulfate composite activator, the density can be improved, the compressive strength can be increased, and the carbon dioxide erosion of the matrix can be reduced by promoting the formation and filling of sodium aluminosilicate gel. Finally, for solid waste cementitious materials in the desulfurized gypsum-slag powder system, this invention provides four sets of examples with different dosages of alkali-sulfate composite activator A (3.5%, 5.0%, 6.5%, and 8.5%). In this embodiment, the alkali-sulfate composite activator was prepared and applied according to the above method. The effects of different dosages of the alkali-sulfate composite activator on solid waste cementitious materials were investigated, and the corresponding material properties of the solid waste cementitious materials were as follows: Figure 6 As can be seen from the comparison, with the increase of the amount of composite activator, the promotion of sodium aluminosilicate gel formation and filling effect is more significant, the strength is further improved, the carbonization depth is further reduced, and the micro-expansion effect is enhanced by the formation of expansive ettringite.

[0023] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An alkali-sulphate composite activator for solid waste cementitious materials, characterised in that, The raw materials include the following weight proportions: a sulfate coagulation-activating component 33-57 parts, an alkali densification-activating component 27-48 parts, and a seed synergistic component 9-21 parts; the sulfate coagulation-activating component includes aluminum sulfate and sodium aluminum sulfate in a mass ratio of 1.5-2.8:1; the alkali densification-activating component includes sodium sulfate and sodium aluminum sulfate in a mass ratio of 1.0-1.8:1; the seed synergistic component is ettringite seed; the dosage of the alkali-sulfate composite activator is 3.5%-8.5% of the total dry mass of the solid waste cementitious material; and the solid waste cementitious material includes industrial by-product gypsum and silico-aluminous solid waste, wherein the industrial by-product gypsum accounts for 30%-70% of the total mass of the cementitious material.

2. The alkali-sulfate composite activator for solid waste cementitious materials according to claim 1, characterized in that, The particle size distribution of the alkali-sulfate composite activator satisfies the following conditions: 100% passes through a 70-micron square-hole sieve, the median particle size D50 is 8-12 microns, and the particle size variation coefficient CV is less than or equal to 5%.

3. The alkali-sulfate composite activator for solid waste cementitious materials according to claim 1, wherein The aluminum sulfate satisfies: specific surface area ≥ 480 m 2 / kg, moisture content ≤ 1.5%, purity ≥ 98.5%.

4. The alkali-sulfate composite activator for solid waste cementitious materials according to claim 1, wherein The sodium sulfate satisfies: specific surface area ≥ 500 m 2 / kg, moisture content ≤ 0.5%, purity ≥ 99.5%.

5. The alkali-sulfate composite activator for solid waste cementitious materials according to claim 1, wherein The sodium aluminum sulfate satisfies: specific surface area ≥ 520 m 2 / kg, moisture content ≤ 1.0%, purity ≥ 96%.

6. The alkali-sulfate composite activator for solid waste cementitious materials according to claim 1, wherein The ettringite crystal seed satisfies: specific surface area ≥ 450 m 2 / kg, median particle size D50 ≤ 6 μm, and intensity ratio of ettringite characteristic peaks in X-ray diffraction spectrum at 2θ ≥ 0.8; the θ is taken as 4.55°, 7.95°, and 10.4°.

7. A method for the preparation of an alkali-sulphate composite activator for solid waste cementitious materials to perform the method according to any one of claims 1-6, characterized in that, The method includes the following steps: S1, raw material pretreatment: dry and grind aluminum sulfate, sodium sulfate, and sodium aluminum sulfate respectively; S2, ettringite seed preparation: dissolve aluminum sulfate, calcium sulfate, and sodium hydroxide in deionized water in a mass ratio of 3.2:2.1:1, first stir and react at 55-65°C for 2-3 hours, then increase the temperature to 70-75°C and continue to react for 1.5-3 hours, control the reaction endpoint pH value to be 10.5-11.5, and obtain ettringite seed through filtration, washing, drying, and grinding; S3, dry material homogenization mixing: first mix the pretreated aluminum sulfate, sodium sulfate, and sodium aluminum sulfate in the designed mass proportions, then add the designed mass of ettringite seed, mix in a mixer at a speed of 300-350 r / min for 35-50 minutes until the variation coefficient of the mixing uniformity is less than or equal to 3%, and package under the protection of inert gas.

8. The method for preparing the alkali-sulfate composite activator for solid waste cementitious materials according to claim 7, characterized in that, In the ettringite seed preparation, the conductivity of the washing liquid of the filter cake after washing is less than or equal to 20 μS / cm.