A slow-setting low-carbon magnesium phosphate composite material and its preparation method

Abstract

A retarded low-carbon magnesium phosphate composite material and its preparation method belong to the field of civil engineering materials. The retarded low-carbon magnesium phosphate composite material includes main components and functional regulating components. The main components are measured by mass percentage as follows: (1) magnesium material 30%-65%, (2) phosphate 25%-40%, (3) mineral admixture 10%-30%, the sum of the three is 100%. In addition, based on the mass of magnesium material in the main components being 100%, additional functional regulating components are added, and the dosage of each component is as follows: (1) dispersant 4%-10%, (2) surfactant 2%-6%, (3) chelating agent 1%-5%, (4) complexing agent 2%-8%, (5) retarder 1%-15%. The specific preparation steps are as follows: ① raw material grinding and ② mixing. The magnesium phosphate composite material of the present invention has the characteristics of long setting time and large adjustable range, and its carbon emission is much lower than that of traditional magnesium phosphate cementitious materials, which has broad application prospects.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering materials, specifically relating to a slow-setting low-carbon magnesium phosphate composite material and its preparation method. Background Technology

[0002] Magnesium phosphate cementitious materials are prepared from calcined magnesium oxide and water-soluble acidic phosphates. They feature rapid setting and hardening, excellent low-temperature strength, high bond strength, low shrinkage, and excellent acid resistance, wear resistance, high-temperature resistance, and freeze-thaw resistance, making them promising for future applications. Currently, magnesium phosphate cementitious materials are mainly used in rapid repair and reinforcement, corrosion and fire retardant coatings, and nuclear waste solidification.

[0003] However, magnesium phosphate cementitious materials still have many problems that restrict their widespread application. These problems are mainly reflected in the following aspects: (1) The setting time is short and difficult to control, making it impossible to carry out construction for a long time. This is because the development of retarders for magnesium phosphate cementitious materials is not perfect, and the retarding effect is significantly affected by the activity of the raw material magnesium oxide; (2) The cost is still high, generally several times that of silicate cement; (3) The raw material magnesium oxide for magnesium phosphate cement needs to be calcined at high temperature, resulting in high carbon emissions and high energy consumption. The carbon emissions per ton of high-temperature calcined magnesium oxide are 2.2-3.1t, which limits its large-scale application; (4) There are a large amount of unreacted high-temperature calcined magnesium oxide in the hardened slurry, which poses a risk of volume stability in the later stage; (5) The strength of magnesium phosphate cementitious materials that have been soaked in water for a long time will shrink slightly.

[0004] Therefore, effectively controlling the setting and hardening time of magnesium phosphate cementitious materials, improving their workability, and reducing carbon emissions during their preparation are of great significance for the promotion and application of magnesium phosphate cementitious materials. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a slow-setting low-carbon magnesium phosphate composite material and its preparation method. Using natural brucite as the magnesium material, it can be directly ground and used without calcination. Simultaneously, the addition of mineral admixtures significantly reduces carbon emissions. The technical solution provided by this invention effectively controls the setting time of the magnesium phosphate composite material while also considering its strength development and reducing carbon emissions during its preparation process. The specific details of this invention are as follows:

[0006] A retarded low-carbon magnesium phosphate composite material, characterized in that the retarded low-carbon magnesium phosphate composite material comprises a main component and a functional regulating component. The main component is measured by mass percentage as follows: (1) magnesium material 30%-65%, (2) phosphate 25%-40%, (3) mineral admixture 10%-30%, the sum of which is 100%. In addition, based on the mass of magnesium material in the main component being 100%, additional functional regulating components are added, with the following dosages for each component: (1) dispersant 4%-10%, (2) surfactant 2%-6%, (3) chelating agent 1%-5%, (4) complexing agent 2%-8%, (5) retarder 1%-15%.

[0007] The magnesium material in the main component is brucite powder with a particle size controlled between 25-150 μm, and the Mg(OH)2 content in the brucite is not less than 87%.

[0008] The phosphate in the main component is prepared by mixing ammonium dihydrogen phosphate and urea phosphate in a mass ratio of 7:3.

[0009] The main components include one or two of the following mineral admixtures: fly ash, mineral powder, and lithium slag. Specifically: the fly ash is grade I or II ash with a particle size range of 10-45 μm; the mineral powder is S75 or S95 grade finely ground water-quenched slag with a particle size range of 10-75 μm; and the lithium slag contains more than 50% SiO2 and Al2O3, with a particle size range of 10-75 μm.

[0010] The dispersant in the functional regulating component is one or two of 2,2-dimethylolpropionic acid, 2,2-dimethylolbutyric acid, and hydroxypropyl methylcellulose.

[0011] The surfactant in the functional regulating component is one or two of sodium di(2-ethylhexyl)succinate sulfonate, sodium fatty alcohol polyoxyethylene ether sulfate, and isooctyl alcohol polyoxyethylene polyoxypropylene ether.

[0012] The chelating agent in the functional regulating component is one or two of the following: disodium methyltriacetate, disodium 1,2-cyclohexanediaminetetraacetate, and diethylenetriaminepentaacetic acid.

[0013] The complexing agent in the functional regulating component is one or two of the following: sodium gluconate dihydrate, di(triethyl)tetraethyldiazapyrrole oxide, and di(ethylene glycol methyl ether)diboron ethylenediamine.

[0014] The retarder in the functional regulating component is myristic acid.

[0015] The preparation steps of the aforementioned retarded low-carbon magnesium phosphate composite material are as follows:

[0016] ① Raw material processing: The magnesium materials and mineral admixtures in the main components are ground and processed.

[0017] ② Mixing: In a mixer, first add magnesium materials and mineral admixtures according to their mass percentage and mix for 5-8 minutes, then add phosphate and mix for 5-8 minutes. Subsequently, based on the mass of magnesium materials in the main components being 100%, additional functional control components are added. Five functional control components are added sequentially, and stirring is required for 3-5 minutes after each addition. Finally, the retarded low-carbon magnesium phosphate composite material is obtained.

[0018] The technical features of this invention are as follows: Addressing the problems of excessively rapid setting time in current magnesium phosphate cementitious materials, leading to poor workability and high carbon emissions, this invention replaces traditionally re-burned magnesium oxide with natural, unburned brucite and mineral admixtures. Functional regulating components effectively control the setting time of the magnesium phosphate composite material while also considering strength development. The retarded low-carbon magnesium phosphate composite material prepared using this invention can have an initial setting time extended to 181 minutes, a 1-day compressive strength of 47.1 MPa, and a 28-day compressive strength as high as 85.4 MPa.

[0019] Specifically, the synergistic regulation mechanism of the performance of the slow-setting low-carbon magnesium phosphate composite material using functional regulating components is as follows: (1) The dispersant contains multiple functional groups and exhibits a strong steric hindrance effect in the magnesium phosphate composite material, enhancing the negative charge on the surface of the particles in the system, causing the particles to move away from each other due to electrostatic repulsion, releasing the water molecules wrapped by the particles to participate in the flow, thereby delaying the setting time of the magnesium phosphate composite material. (2) The surfactant is an anionic surfactant. The surface of magnesium material has a high positive charge. The surfactant used can be adsorbed on the surface of magnesium material, hindering the contact between magnesium material and phosphate, slowing down the dissolution rate of magnesium material, thereby delaying the setting time of the magnesium phosphate composite material. (3) Both chelating agents and complexing agents can react with Mg 2+ The combination of salts reduces the Mg content in the system. 2+ The concentration slowed down the formation and crystal growth of phosphate crystals, which are hydration products, thereby delaying the setting time of magnesium phosphate composites. (4) The retarder is a low-temperature phase change material. The reaction of magnesium phosphate composites is an exothermic reaction. As the temperature rises, the retarder undergoes a phase change. This process is an endothermic reaction, which consumes the heat of hydration of magnesium phosphate composites and alleviates the continuous rise in system temperature, thereby delaying the setting time of magnesium phosphate composites.

[0020] On the one hand, the mineral admixtures effectively fill the pores of the magnesium phosphate composite material, improve the pore size distribution, reduce the porosity, and increase the structural density, thereby improving the strength of the magnesium phosphate composite material. On the other hand, the SiO2, Al2O3, and CaO in the mineral admixtures can react with phosphates to generate amorphous aluminum phosphate and calcium phosphate gels, ensuring the development of the strength of the magnesium phosphate composite material in the later stage.

[0021] This invention exhibits a significant low-carbon effect compared to traditional magnesium phosphate cementitious materials. The carbon emissions per ton of high-temperature calcined magnesium oxide are 2.2-3.1 t, per ton of phosphate is 1.7-2.3 t, and per ton of borax is 1.5-2.5 t. Therefore, the carbon emissions of traditional magnesium phosphate cementitious materials with 10%-30% admixtures are calculated to be 1.5-2.0 t. The carbon emissions from the crushing and grinding process of brucite are 0.03 t. The carbon emissions of the retarded low-carbon magnesium phosphate composite material prepared by this invention are 0.5-0.7 t, representing a 50%-70% reduction in carbon emissions compared to traditional magnesium phosphate cementitious materials.

[0022] The beneficial technical effects of this invention are as follows: the setting time of magnesium phosphate composite material is controllable, the hydration heat release is low, the early strength is high, and the later strength continues to increase. The replacement of magnesium oxide with brucite and mineral admixtures greatly reduces the carbon emissions of magnesium phosphate cementitious materials, enriches the application scenarios of magnesium phosphate cementitious materials, and promotes the transformation of its research from preparation technology to application technology. It is of great significance for further improving the comprehensive utilization level of bulk solid waste, comprehensively improving resource utilization efficiency, implementing the national requirements for energy conservation and emission reduction, resource conservation and utilization, and environmental protection, and promoting high-quality development. Detailed Implementation

[0023] To make the technical means, innovative features, objectives and effects of this invention easier to understand, the invention will be further described below.

[0024] The embodiments described herein are specific implementations of the present invention, used to illustrate the concept of the invention, and are illustrative and exemplary, and should not be construed as limiting the implementation or scope of the invention. In addition to the embodiments described herein, those skilled in the art can employ other obvious technical solutions based on the content disclosed in the claims and specification of this application. These technical solutions include those that make any obvious substitutions and modifications to the embodiments described herein.

[0025] To further demonstrate the effects of this invention, specific examples are provided below for detailed explanation. The specific details and technical effects of each example are as follows.

[0026] Example 1 illustrates a retarded low-carbon magnesium phosphate composite material and its preparation method disclosed in this invention. The raw materials for the main components are weighed according to their mass percentages. The functional regulating component is added additionally, calculated as 100% of the magnesium material in the main components. All components are of industrial grade purity. Details are as follows:

[0027] Components mass percentage Brucite 65.0％ Ammonium dihydrogen phosphate 17.5％ Urea phosphate 7.5％ lithium slag 10.0％ 2,2-Dimethylolpropionic acid 7.0％ Sodium di(2-ethylhexyl)succinate sulfonate 4.0％ Disodium hydantoin 3.0％ Sodium gluconate dihydrate 5.0％ Myristic acid 8.0％

[0028] In this example, the brucite used contained 87% Mg(OH)2 with a particle size range of 25-150 μm; the lithium slag contained 50.3% SiO2 and Al2O3 with a particle size range of 10-75 μm. The brucite powder was placed in a mixer, and lithium slag was added first and stirred for 5 min according to a mass percentage. Then, ammonium dihydrogen phosphate and urea phosphate were added and stirred for 5 min. Subsequently, based on 100% magnesium material in the main components, functional regulating components were added according to a specified mass percentage. The order of addition was as follows: first, sodium di(2-ethylhexyl)succinate sulfonate was added and stirred for 5 min; then, 2,2-dimethylolpropionic acid was added and stirred for 5 min; then, disodium thiamintriacetate was added and stirred for 5 min; then, sodium gluconate dihydrate was added and stirred for 5 min; finally, myristic acid was added and stirred for another 5 min to obtain the retarded low-carbon magnesium phosphate composite material.

[0029] Example 2 illustrates a retarded low-carbon magnesium phosphate composite material and its preparation method disclosed in this invention. The raw materials for the main components are weighed according to their mass percentages. The functional regulating component is added additionally, calculated as 100% of the magnesium material in the main components. All components are of industrial grade purity. Details are as follows:

[0030] Components mass percentage Brucite 48.0％ Ammonium dihydrogen phosphate 22.4％ Urea phosphate 9.6％ Mineral powder 20.0％ 2,2-Dihydroxymethylbutyric acid 8.0％ Sodium fatty alcohol polyoxyethylene ether sulfate 3.0％ Disodium 1,2-cyclohexanediaminetetraacetate 2.0％ Di(triethyl)tetraethyldiazapyrrole oxide 6.0％ Myristic acid 9.0％

[0031] The brucite used in this example has a Mg(OH)2 content of 91% and a particle size range of 25-150 μm; the mineral powder is S95 grade finely ground water-quenched slag with a particle size range of 10-75 μm. The brucite powder was placed in a mixer, and the mineral powder was added first according to the mass percentage and stirred for 5 min. Then, ammonium dihydrogen phosphate and urea phosphate were added and stirred for 5 min. Subsequently, based on the mass of magnesium material in the main components being 100%, functional regulating components were added according to the specified mass percentage. The order of addition was as follows: first, disodium 1,2-cyclohexanediaminetetraacetate was added and stirred for 5 min; then, sodium fatty alcohol polyoxyethylene ether sulfate was added and stirred for 5 min; then, 2,2-dimethylolbutyric acid was added and stirred for 5 min; then, di(triethyl)tetraethyldiazapyrrole oxide was added and stirred for 5 min; finally, myristic acid was added and stirred for another 5 min to obtain the retarded low-carbon magnesium phosphate composite material.

[0032] Example 3 illustrates a retarded low-carbon magnesium phosphate composite material and its preparation method disclosed in this invention. The raw materials for the main components are weighed according to their mass percentages. The functional regulating component is added additionally, calculated as 100% of the magnesium material in the main components. All components are of industrial grade purity. Details are as follows:

[0033] Components mass percentage Brucite 30.0％ Ammonium dihydrogen phosphate 28.0％ Urea phosphate 12.0％ fly ash 30.0％ Hydroxypropyl methylcellulose 6.0％ Isooctyl alcohol polyoxyethylene polyoxypropylene ether 5.0％ Diethylenetriaminepentaacetic acid 4.0％ Di(ethylene glycol methyl ether)diboron-ethylenediamine 4.0％ Myristic acid 10.0％

[0034] In this example, the brucite used has a Mg(OH)₂ content of 89% and a particle size range of 25-150 μm; the fly ash is grade II ash with a particle size range of 10-45 μm. The brucite powder was placed in a mixer, and fly ash was added first according to a mass percentage and mixed for 5 min. Then, ammonium dihydrogen phosphate and urea phosphate were added and mixed for 5 min. Subsequently, based on the mass of magnesium material in the main components being 100%, functional regulating components were added according to a specified mass percentage. The order of addition was as follows: first, hydroxypropyl methyl cellulose myristate was added and mixed for 5 min; then, isooctyl alcohol polyoxyethylene polyoxypropylene ether was added and mixed for 5 min; then, diethylenetriaminepentaacetic acid was added and mixed for 5 min; then, di(ethylene glycol methyl ether) diboron ethylenediamine was added and mixed for 5 min; finally, hydroxypropyl methyl cellulose was added and mixed for another 5 min to obtain the retarded low-carbon magnesium phosphate composite material.

[0035] Example 4 illustrates a retarded low-carbon magnesium phosphate composite material and its preparation method disclosed in this invention. The raw materials for the main components are weighed according to their mass percentages. The functional regulating component is added additionally, calculated as 100% of the magnesium material in the main components. All components are of industrial grade purity. Details are as follows:

[0036] Components mass percentage Brucite 48.0％ Ammonium dihydrogen phosphate 22.4％ Urea phosphate 9.6％ lithium slag 10.0％ fly ash 10.0％ 2,2-Dimethylolpropionic acid 4.0％ Hydroxypropyl methylcellulose 2.0％ Sodium di(2-ethylhexyl)succinate sulfonate 1.0％ Isooctyl alcohol polyoxyethylene polyoxypropylene ether 2.0％ Disodium hydantoin 1.0％ Sodium gluconate dihydrate 2.0％ Myristic acid 1.0％

[0037] In this example, the brucite used contained 92% Mg(OH)2 with a particle size range of 25-150 μm; the lithium slag contained 55.4% SiO2 and Al2O3 with a particle size range of 10-75 μm; and the fly ash was grade I ash with a particle size range of 10-45 μm. The brucite powder was placed in a mixer, and lithium slag and fly ash were added according to their mass percentages and mixed for 5 minutes. Then, ammonium dihydrogen phosphate and urea phosphate were added and mixed for another 5 minutes. Subsequently, based on the mass of magnesium material in the main components being 100%, functional regulating components were added in the prescribed mass percentage. The order of addition was as follows: first, 2,2-dimethylolpropionic acid and hydroxypropyl methylcellulose were added and stirred for 5 minutes; then, sodium di(2-ethylhexyl)succinate sulfonate and isooctyl alcohol polyoxyethylene polyoxypropylene ether were added and stirred for 5 minutes; then, disodium thiamintriacetate was added and stirred for 5 minutes; then, sodium gluconate dihydrate was added and stirred for 5 minutes; finally, myristic acid was added and stirred for another 5 minutes to obtain the retarded low-carbon magnesium phosphate composite material.

[0038] Example 5 illustrates a retarded low-carbon magnesium phosphate composite material and its preparation method disclosed in this invention. The raw materials for the main components are weighed according to their mass percentages. The functional regulating component is added additionally, calculated as 100% of the magnesium material in the main components. All components are of industrial grade purity. Details are as follows:

[0039] Components mass percentage Brucite 48.0％ Ammonium dihydrogen phosphate 22.4％ Urea phosphate 9.6％ lithium slag 10.0％ Mineral powder 10.0％ 2,2-Dimethylolpropionic acid 10.0％ Sodium di(2-ethylhexyl)succinate sulfonate 6.0％ Disodium hydantoin 2.5％ Disodium 1,2-cyclohexanediaminetetraacetate 2.5％ Sodium gluconate dihydrate 4.0％ Di(triethyl)tetraethyldiazapyrrole oxide 4.0％ Myristic acid 15.0％

[0040] In this example, the brucite used contained 93% Mg(OH)2 with a particle size range of 25-150 μm; the lithium slag contained 58.1% SiO2 and Al2O3 with a particle size range of 10-75 μm; and the mineral powder was S75 grade finely ground water-quenched slag with a particle size range of 10-75 μm. The brucite powder was placed in a mixer, and lithium slag and mineral powder were added first according to their mass percentages and mixed for 5 minutes. Then, ammonium dihydrogen phosphate and urea phosphate were added and mixed for another 5 minutes. Subsequently, based on the mass of magnesium material in the main components being 100%, functional regulating components were added in the prescribed mass percentage. The order of addition was as follows: first, 2,2-dimethylolpropionic acid was added and stirred for 5 min; then, sodium di(2-ethylhexyl)succinate sulfonate was added and stirred for 5 min; then, disodium thiamintriacetate and disodium 1,2-cyclohexanediaminetetraacetate were added and stirred for 5 min; then, sodium gluconate dihydrate and di(triethyl)tetraethyldiazapyrrole oxide were added and stirred for 5 min; finally, myristic acid was added and stirred for another 5 min to obtain the retarded low-carbon magnesium phosphate composite material.

[0041] Comparative Example 1

[0042] In this comparative example, brucite was replaced with magnesium oxide calcined at 1600℃, and borax was added additionally based on 100% of the mass of magnesium oxide, with industrial grade purity, as detailed below:

[0043] Components mass percentage magnesium oxide 40.0％ Ammonium dihydrogen phosphate 30.0％ fly ash 30.0％ Borax 5.0％

[0044] Performance testing

[0045] Samples of the magnesium phosphate composite materials prepared by Examples 1-5 and Comparative Example 1 were taken and the following performance tests were conducted on the samples.

[0046] The initial setting time of the samples in Examples 1-5 and Comparative Example 1 was tested according to GB / T1346-2011; the 1-day compressive strength and 28-day compressive strength of the magnesium phosphate composite material were tested according to JC / T2537-2019 "Magnesium Phosphate Repair Mortar". When preparing the slurry, the mass ratio of water to the main components of the magnesium phosphate composite material (magnesium materials, phosphate, and mineral admixtures) was 0.16:1.

[0047] Table 1 - Performance test data of samples from Examples 1-5 and Comparative Example 1

[0048]

[0049] This invention uses natural non-fired brucite and mineral admixtures to replace traditional refired magnesium oxide. Under the synergistic effect of functional regulating components, the setting time of magnesium phosphate composite materials in Examples 1-5 is significantly extended to more than 150 min, the 1-day compressive strength exceeds 40 MPa, and the 28-day compressive strength exceeds 62.5 MPa. The technology of this invention achieves the synergistic development of setting time and mechanical properties of magnesium phosphate composite materials.

[0050] According to the sample test data of Examples 1-5 and Comparative Example 1 in Table 1, the setting time of the magnesium phosphate composite material prepared by this invention is extended by 665.0%-1135.0% compared with that of traditional magnesium phosphate cementitious materials, the 1-day compressive strength is increased by 5.0%-36.0%, and the 28-day compressive strength is increased by 5.6%-44.0%. Compared with traditional magnesium phosphate cementitious materials, the carbon emissions of the magnesium phosphate composite material prepared by this invention are reduced by 50%-70%.

[0051] The above embodiments are only used to explain the present invention and do not constitute a limitation on the scope of the claims. Other alternative means that can be conceived by those skilled in the art based on the content of the present invention should be within the protection scope of the claims of the present invention.

[0052] The slow-setting low-carbon magnesium phosphate composite material of the present invention has a wide range of adjustable setting time and excellent strength performance. According to the actual needs of the on-site project, the mass ratio of magnesium material to phosphate, the amount of mineral admixtures, and the amount of functional control components can be adjusted to obtain a magnesium phosphate composite material with better comprehensive performance.

Claims

1. A retarded low-carbon magnesium phosphate composite material, characterized in that, The retarded low-carbon magnesium phosphate composite material includes a main component and a functional regulating component; the main component is measured by mass percentage as follows: (1) magnesium material 30%-65%, (2) phosphate 25%-40%, (3) mineral admixture 10%-30%, the sum of the three is 100%; in addition, based on the mass of magnesium material in the main component being 100%, additional functional regulating components are added, and the dosage of each component is as follows: (1) dispersant 4%-10%, (2) surfactant 2%-6%, (3) chelating agent 1%-5%, (4) complexing agent 2%-8%, (5) retarder 1%-15%; the magnesium material in the main component is brucite powder, the particle size is controlled at 25-150μm, and the Mg(OH)2 content in brucite is not less than 87%; The phosphate in the main component is prepared by mixing ammonium dihydrogen phosphate and urea phosphate in a mass ratio of 7:

3. The dispersant in the functional regulating component is one or two of 2,2-dimethylolpropionic acid, 2,2-dimethylolbutyric acid, and hydroxypropyl methylcellulose. The surfactant in the functional regulating component is one or two of sodium di(2-ethylhexyl)succinate sulfonate, sodium fatty alcohol polyoxyethylene ether sulfate, and isooctyl alcohol polyoxyethylene polyoxypropylene ether. The chelating agent in the functional regulating component is one or two of the following: disodium methyltriacetate, disodium 1,2-cyclohexanediaminetetraacetate, and diethylenetriaminepentaacetic acid. The complexing agent in the functional regulating component is one or two of the following: sodium gluconate dihydrate, di(triethyl)tetraethyldiazapyrrole oxide, and di(ethylene glycol methyl ether)diboron ethylenediamine. The retarder in the functional regulating component is myristic acid.

2. The retarded low-carbon magnesium phosphate composite material according to claim 1, characterized in that: The main components include one or two of the following mineral admixtures: fly ash, mineral powder, and lithium slag; wherein: the fly ash is grade I or grade II ash with a particle size range of 10-45 μm; the mineral powder is S75 or S95 grade finely ground water-quenched slag with a particle size range of 10-75 μm; and the lithium slag contains more than 50% SiO2 and Al2O3 with a particle size range of 10-75 μm.

3. A method for preparing the retarded low-carbon magnesium phosphate composite material as described in claim 1 or 2, characterized in that, The steps are as follows: ① Raw material processing: The magnesium materials and mineral admixtures in the main components are ground and processed; ② Mixing: In a mixer, first add magnesium materials and mineral admixtures according to mass percentage and mix for 5-8 minutes, then add phosphate and mix for 5-8 minutes; subsequently, based on the mass of magnesium materials in the main components being 100%, add additional functional control components. Five functional control components are added in sequence, and each time a functional control component is added, it needs to be stirred for 3-5 minutes. Finally, the retarded low-carbon magnesium phosphate composite material is obtained.

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