Glass ceramic for temperature measurement and preparation method thereof

By using high silicon-based glass as the matrix material, a temperature measurement microcrystalline glass with a crystallization temperature of 400-580℃ was prepared, which solved the problem of high cost caused by the use of rare earth luminescent materials in the prior art, and achieved cost reduction and temperature measurement sensitivity Improved effect.

CN119430659APending Publication Date: 2025-02-14SHENZHEN XIANGTONG PHOTOELECTRIC TECH
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Patent Information

Application Number
CN202411574230.9
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-06
Publication Date
2025-02-14

AI Technical Summary

Technical Problem

Existing microcrystalline glasses for temperature measurement require the use of rare earth luminescent materials, resulting in higher costs.

Method used

High silicon-based glass is used as the matrix material, and through the adjustment of material composition and preparation process, a temperature measurement microcrystalline glass with a crystallization temperature of 400-580℃ is prepared to replace rare earth luminescent materials.

Benefits of technology

The production cost of temperature measurement bricks is reduced, and the material is stable in an oxidation or reduction environment, and has high temperature measurement sensitivity and high temperature resistance.

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Abstract

The invention discloses microcrystalline glass for temperature measurement and a preparation method thereof, and the crystallization temperature of the microcrystalline glass for temperature measurement is 400-580 DEG C; the glass ceramic for temperature measurement comprises the following components in percentage by mass: 60-80% of silicon dioxide, 10-20% of lithium oxide, 3-8% of phosphorus pentoxide, 3-10% of sodium oxide and potassium oxide, 1-6% of aluminum oxide, 1-4% of zirconium oxide, 1-5% of cerium oxide and 0.5-3% of a vanadium compound. According to the invention, the high-silicon-based glass is used as a base material, so that the glass ceramic for temperature measurement has relatively strong inertia and can stably exist in an oxidation or reduction environment. A traditional material is adopted to replace a rare earth luminescent material, and raw materials are low in price and have no other special requirements.
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Description

Technical Field

[0001] The present invention relates to the technical field of temperature sensing, and in particular to a microcrystalline glass for temperature measurement and a preparation method thereof. Background Art

[0002] Thermo-measuring bricks are a special material used for temperature measurement in high-temperature environments. They are usually used in industrial furnaces, especially in the ceramic, glass, metallurgical and other industries. Thermo-measuring bricks can work for a long time in a high-temperature environment without obvious physical or chemical changes, thus accurately reflecting the temperature changes in the furnace.

[0003] A certain amount of rare earth luminescent materials are used in the materials of existing temperature measuring bricks, which leads to high production and processing costs and also has some limitations on the use environment.

[0004] Therefore, the prior art needs to be further improved and enhanced. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a microcrystalline glass for temperature measurement and a preparation method thereof, aiming to solve the problem that the existing microcrystalline glass for temperature measurement requires the use of rare earth luminescent materials, resulting in high cost of temperature measuring bricks.

[0006] The technical solution adopted by the present invention to solve the above technical problems is as follows:

[0007] In a first aspect, a method for preparing microcrystalline glass for temperature measurement, wherein the crystallization temperature of the microcrystalline glass for temperature measurement is 400-580°C; the microcrystalline glass for temperature measurement contains, by mass percentage: 60-80% silicon dioxide, 10-20% lithium oxide, 3-8% phosphorus pentoxide, 3-10% sodium oxide and potassium oxide, 1-6% aluminum oxide, 1-4% zirconium oxide, 1-5% cerium oxide, and 0.5-3% vanadium compounds.

[0008] The following are preferred technical solutions of the present invention, but are not intended to limit the technical solutions provided by the present invention. Through the following preferred technical solutions, the objectives and beneficial effects of the present invention can be better achieved and realized.

[0009] As a preferred technical solution, the microcrystalline glass for temperature measurement, wherein the crystallization temperature of the microcrystalline glass for temperature measurement is 450-500°C; measured by mass percentage, the microcrystalline glass for temperature measurement includes: 70-75% silicon dioxide, 15-20% lithium oxide, 5-8% phosphorus pentoxide, 6-10% sodium oxide and potassium oxide, 1-4% aluminum oxide, 1-4% zirconium oxide, 1-3% cerium oxide, and 1-2% vanadium compound.

[0010] In a second aspect, a method for preparing the temperature measuring glass-ceramics according to the first aspect, comprising:

[0011] Obtain glass raw materials, which include, by mass percentage, 60-80% silicon dioxide, 10-20% lithium oxide, 3-8% phosphorus pentoxide, 3-10% sodium oxide and potassium oxide, 1-6% aluminum oxide, 1-4% zirconium oxide, 1-5% cerium oxide, and 0.5-3% vanadium compound;

[0012] The glass raw materials are melted at a temperature of 1450-1700° C. and subjected to clarification treatment to obtain a glass melt;

[0013] Casting the molten glass into a shape to obtain a basic glass;

[0014] The base glass is microcrystallized to obtain the microcrystalline glass for temperature measurement.

[0015] As a preferred technical solution, the method for preparing microcrystalline glass for temperature measurement, wherein the step of obtaining glass raw materials specifically includes:

[0016] The silicon dioxide, lithium oxide, phosphorus pentoxide, sodium oxide and potassium oxide, aluminum oxide, zirconium oxide, cerium oxide and vanadium compound are weighed according to the addition ratio, mixed evenly and then ground to obtain the glass raw material, wherein the grinding time is 30-35 minutes and the particle size after grinding is 10-35 microns.

[0017] As a preferred technical solution, the method for preparing the temperature-measuring glass-ceramics, wherein the glass raw materials are melted at a temperature of 1450-1700° C., specifically comprises:

[0018] The glass raw materials are placed in a crucible, and the crucible is placed in a heating device, and the temperature is increased to 800-1200° C. at a rate of 10-15° C. / min, and then increased to 1450-1700° C. at a rate of 3-5° C. / min, and kept at this temperature for 0.5-5 hours.

[0019] As a preferred technical solution, the method for preparing the temperature measuring glass-ceramics, wherein the glass melt is cast into a shape to obtain a basic glass, specifically comprises:

[0020] The molten glass is poured into a preheated mold, and the mold is placed in a muffle furnace heated to 500-520° C. and kept warm for 2.5-3 hours, and then cooled to room temperature to obtain the basic glass.

[0021] As a preferred technical solution, the method for preparing the temperature-measuring glass-ceramics, wherein the base glass is subjected to microcrystallization treatment to obtain the temperature-measuring glass-ceramics, specifically comprises:

[0022] The base glass is placed in a heating device, heated to 400-580° C., and kept warm for 2-3 hours to obtain the temperature-measuring microcrystalline glass.

[0023] As a preferred technical solution, the method for preparing microcrystalline glass for temperature measurement, wherein the temperature is raised to 400-580°C, wherein the heating rate is 1-5°C / min.

[0024] As a preferred technical solution, the temperature measuring glass-ceramic is square or round in shape; the volume of the temperature measuring glass-ceramic is greater than 0.5 cm 3 Less than 2cm 3 .

[0025] Beneficial effects: Compared with the prior art, the present invention adopts high-silicon-based glass as the matrix material, so that the temperature-measuring microcrystalline glass has strong inertness and can exist stably in an oxidizing or reducing environment. Traditional materials are used to replace rare earth luminescent materials, and the raw materials are cheap and have no other special requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a picture of the color change of the microcrystalline glass for temperature measurement provided by the present invention at different temperature ranges;

[0027] Figure 2 The present invention provides a picture of the color change and transparency of the microcrystalline glass for temperature measurement in the temperature range of 770-820°C. DETAILED DESCRIPTION

[0028] The present invention provides a glass-ceramic for temperature measurement and a preparation method thereof. To make the purpose, technical solution and effect of the present invention clearer and more specific, the present invention is further described in detail below. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0029] It will be understood by those skilled in the art that, unless otherwise stated, the singular forms "a", "an", "said" and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present application refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations. It should be understood that the term "and / or" used herein includes all or any unit and all combinations of one or more associated listed items.

[0030] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art to which this application belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with those in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless specifically defined as here.

[0031] It should be understood that the sequence number and size of each step in this embodiment do not mean the order of execution, and the execution order of each process is determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of this application. All instruments used are commercially available products.

[0032] The microcrystalline glass for temperature measurement provided by the present invention comprises: 60-80% silicon dioxide, 10-20% lithium oxide, 3-8% phosphorus pentoxide, 3-10% sodium oxide and potassium oxide, 1-6% aluminum oxide, 1-4% zirconium oxide, 1-5% cerium oxide, and 0.5-3% vanadium compound. The microcrystalline glass is obtained by crystallization at a crystallization temperature of 400-580°C. The corresponding raw materials are carbonates or compounds corresponding to the oxides themselves, and are not limited to their sulfates or nitrates. Silicon dioxide and lithium oxide are the main formers of different types of crystals, phosphorus pentoxide is a nucleating agent participating in the formation of crystals, alkali metals are used to reduce the melting and clarifying temperature of the glass liquid, zirconium oxide and aluminum oxide are used to improve the strength of the material matrix, cerium oxide and vanadium compounds are the main components for color development and discoloration, and other oxides are used for fine-tuning of temperature and color.

[0033] The microcrystalline glass provided by the present invention has strong stability, can be used in an oxidizing or reducing environment, is not affected by other environmental fields, and can be designed according to actual conditions. The raw material price is cheap and no other special requirements are required. When measuring temperature, nonlinear temperature measurement is used, and no extra insulation time is required.

[0034] In one implementation of the present invention, the crystallization temperature of the temperature-measuring glass-ceramics is 450-500°C; by mass percentage, the temperature-measuring glass-ceramics includes: 70-75% silicon dioxide, 15-20% lithium oxide, 5-8% phosphorus pentoxide, 6-10% sodium oxide and potassium oxide, 1-4% aluminum oxide, 1-4% zirconium oxide, 1-3% cerium oxide, and 1-2% vanadium compound. Controlling the crystallization temperature of the glass-ceramics at 450-500°C is more conducive to the growth of the crystal nucleus and can improve the sensitivity of the glass-ceramics to temperature.

[0035] Based on the same inventive concept, the present invention also provides a method for preparing a temperature-measuring glass-ceramic, comprising the following steps:

[0036] S10, obtaining glass raw materials, wherein the glass raw materials include, by mass percentage, 60-80% silicon dioxide, 10-20% lithium oxide, 3-8% phosphorus pentoxide, 3-10% sodium oxide and potassium oxide, 1-6% aluminum oxide, 1-4% zirconium oxide, 1-5% cerium oxide, and 0.5-3% vanadium compound;

[0037] S20, melting the glass raw materials at a temperature of 1450-1700° C. and performing clarification treatment to obtain a glass melt;

[0038] S30, casting the molten glass into a shape to obtain a basic glass;

[0039] S40, performing microcrystallization treatment on the base glass to obtain the microcrystal glass for temperature measurement.

[0040] In the present invention, high silicon base glass is first prepared, and then the prepared high silicon base glass is microcrystallized to obtain microcrystalline glass for temperature measurement. Among them, melting and clarification, the melting process is not set (float method, Czochralski method, crucible furnace, etc. can be prepared), the melting temperature is 1450-1700℃, the melting time is determined according to the melting process, and the glass liquid is required to have uniform texture and no bubbles inside. There is no special requirement for the molding shape, and it can be specially customized, preferably 0.5≤ volume≤2cm 2 Square or circular structure; microcrystallization temperature requirement: 400-580℃, duration 6-36h, to facilitate the full growth of microcrystalline nuclei and improve sensitivity to temperature.

[0041] The above technical solution provided by the present invention is further explained below through a specific preparation method.

[0042] Example 1

[0043] (1) Mixing of raw materials: by mass percentage: 55% silicon dioxide, 28% lithium carbonate, 4.5% diammonium phosphate, 3.5% potassium carbonate, 1% sodium carbonate, 2% aluminum oxide, 1% zirconium oxide, 1.5% cerium oxide, 0.5% vanadium compound, and 3% other raw materials. Weigh 500 g of the raw materials and put them into a mixer for 1 hour to mix them thoroughly.

[0044] (2) Melting of the matrix glass: Pour the mixed materials in (1) into a 300 ml platinum crucible, and then place the platinum crucible into a high-temperature furnace. First, heat the temperature to 1200°C at a rate of 10°C / min and keep it warm for 30 minutes. Then, heat the temperature to 1530°C at a rate of 5°C / min and keep it warm for 120 minutes to complete the melting of the glass liquid.

[0045] (3) Basic glass molding: Pour the glass liquid in (2) quickly into the mold preheated at 300°C and cool naturally to form the mold. The mold size is 15*15*15mm in length, width and height.

[0046] (4) Microcrystallization treatment: The glass block described in (3) is placed in a heat treatment furnace, heated to 500°C at a heating rate of 5°C / min, and then kept at this temperature for 2 hours. The temperature is then cooled to room temperature at a cooling rate of 5°C / min to obtain a light yellow transparent microcrystallized glass block.

[0047] Example 2

[0048] (1) Mixing of raw materials: by mass percentage: 60% silicon dioxide, 10% lithium carbonate, 4.5% diammonium phosphate, 1.5% potassium carbonate, 1.5% sodium carbonate, 1% aluminum oxide, 1% zirconium oxide, 1% cerium oxide, 0.5% vanadium compound, and 3% other raw materials. Weigh 500 g of the raw materials and put them into a mixer for 1 hour to mix them thoroughly.

[0049] (2) Melting of the matrix glass: Pour the mixed materials in (1) into a 300 ml platinum crucible, and then place the platinum crucible into a high-temperature furnace. First, heat the temperature to 800°C at a rate of 10°C / min and keep it warm for 30 minutes. Then, heat the temperature to 1450°C at a rate of 5°C / min and keep it warm for 120 minutes to complete the melting of the glass liquid.

[0050] (3) Basic glass molding: Pour the glass liquid in (2) quickly into the mold preheated at 300°C and cool naturally to form the mold. The mold size is 15*15*15mm in length, width and height.

[0051] (4) Microcrystallization treatment: The glass block described in (3) is placed in a heat treatment furnace, heated to 400°C at a heating rate of 1°C / min, and then kept at this temperature for 2 hours. The temperature is then cooled to room temperature at a cooling rate of 5°C / min, to obtain a light yellow transparent microcrystallized glass block.

[0052] Example 3

[0053] (1) Mixing of raw materials: by mass percentage: 80% silicon dioxide, 20% lithium carbonate, 4.5% diammonium phosphate, 6.5% potassium carbonate, 3.5% sodium carbonate, 6% aluminum oxide, 4% zirconium oxide, 5% cerium oxide, 3% vanadium compound, and 1% other raw materials. Weigh 500 g of the raw materials and put them into a mixer for 1 hour to mix them thoroughly.

[0054] (2) Melting of matrix glass: Pour the mixed materials in (1) into a 300 ml platinum crucible, and then place the platinum crucible into a high temperature furnace. First, heat the temperature to 1200°C at a rate of 15°C / min and keep it at that temperature for 30 minutes. Then, heat the temperature to 1700°C at a rate of 5°C / min and keep it at that temperature for 300 minutes to complete the melting of the glass liquid.

[0055] (3) Basic glass molding: Pour the glass liquid in (2) quickly into the mold preheated at 300°C and cool naturally to form. The mold size is 15*15*15mm in length, width and height.

[0056] (4) Microcrystallization treatment: The glass block described in (3) was placed in a heat treatment furnace, heated to 580°C at a heating rate of 5°C / min, and then kept at that temperature for 5 hours. The temperature was then cooled to room temperature at a cooling rate of 5°C / min to obtain a light yellow transparent microcrystallized glass block.

[0057] Example 4

[0058] (1) Mixing of raw materials: by mass percentage: 70% silicon dioxide, 15% lithium carbonate, 3.5% diammonium phosphate, 5.5% potassium carbonate, 1.5% sodium carbonate, 4% aluminum oxide, 4% zirconium oxide, 3% cerium oxide, 2% vanadium compound, and 3% other raw materials. Weigh 500 g of the raw materials and put them into a mixer for 1 hour to mix them thoroughly.

[0059] (2) Melting of matrix glass: Pour the mixed materials in (1) into a 300 ml platinum crucible, and then place the platinum crucible into a high temperature furnace. First, heat the temperature to 1000°C at a rate of 10°C / min and keep it at that temperature for 30 minutes. Then, heat the temperature to 1600°C at a rate of 5°C / min and keep it at that temperature for 300 minutes to complete the melting of the glass liquid.

[0060] (3) Basic glass molding: Pour the glass liquid in (2) quickly into the mold preheated at 300°C and cool naturally to form. The mold size is 15*15*15mm in length, width and height.

[0061] (4) Microcrystallization treatment: The glass block described in (3) is placed in a heat treatment furnace, heated to 450°C at a heating rate of 5°C / min, and then kept at this temperature for 5 hours. The temperature is then cooled to room temperature at a cooling rate of 5°C / min to obtain a light yellow transparent microcrystallized glass block.

[0062] Example 5

[0063] (1) Mixing of raw materials: by mass percentage: 75% silicon dioxide, 20% lithium carbonate, 4.5% diammonium phosphate, 6.5% potassium carbonate, 3.5% sodium carbonate, 4% aluminum oxide, 4% zirconium oxide, 3% cerium oxide, 2% vanadium compound, and 1% other raw materials. Weigh 500 g of the raw materials and put them into a mixer for 1 hour to mix them thoroughly.

[0064] (2) Melting of matrix glass: Pour the mixed materials in (1) into a 300 ml platinum crucible, and then place the platinum crucible into a high temperature furnace. First, heat the temperature to 1200°C at a rate of 15°C / min and keep it at that temperature for 30 minutes. Then, heat the temperature to 1700°C at a rate of 5°C / min and keep it at that temperature for 300 minutes to complete the melting of the glass liquid.

[0065] (3) Basic glass molding: Pour the glass liquid in (2) quickly into the mold preheated at 300°C and cool naturally to form the mold. The mold size is 15*15*15mm in length, width and height.

[0066] (4) Microcrystallization treatment: The glass block described in (3) was placed in a heat treatment furnace, heated to 580°C at a heating rate of 5°C / min, and then kept at that temperature for 5 hours. The temperature was then cooled to room temperature at a cooling rate of 5°C / min to obtain a light yellow transparent microcrystallized glass block.

[0067] The transparent microcrystalline glass prepared in the above example was processed into 10*10*10 mm bricks for temperature measurement. The color changes of the material in different temperature ranges were as follows: Figure 1 It can be clearly seen that at different temperatures, the color changes are obvious, indicating that the temperature-measuring microcrystalline glass provided by the present invention has a high temperature measurement sensitivity.

[0068] The microcrystalline glass prepared in Example 1 was processed into bricks with a size of 10*10*10 mm and the color changed as follows at a temperature of 770-820°C: Figure 2 As shown, as the temperature rises, the color gradually darkens, and a temperature difference of 10°C can be clearly distinguished (without the aid of instruments, it can be distinguished visually).

[0069] In summary, the present invention provides a microcrystalline glass for temperature measurement and a preparation method thereof, wherein the crystallization temperature of the microcrystalline glass for temperature measurement is 400-580°C; in terms of mass percentage, the microcrystalline glass for temperature measurement contains: 60-80% silicon dioxide, 10-20% lithium oxide, 3-8% phosphorus pentoxide, 3-10% sodium oxide, 1-6% aluminum oxide, 1-4% zirconium oxide, 1-3% cerium oxide, and 1-2% vanadium compound. The present invention adopts high-silicon-based glass as a matrix material, and the matrix material is high-silicon glass, which has strong inertness and can stably exist in an oxidizing or reducing environment, and can maintain a good appearance within 900°C. Nonlinear temperature measurement does not require extra insulation time. The corresponding temperature can be measured after the material is stable as a whole. Taking a 10*10*10mm material as an example, the corresponding ambient temperature can be measured by basically keeping warm for 5-8min. Different temperature measurement times exist according to the size of the temperature measurement material. The preferred volume is less than 1 cubic centimeter. At this time, the temperature measurement and insulation time can be controlled within 10min. Moreover, the matrix material is glass material, and the glass tailings and waste can be melted back into the furnace for many times. The batch production technology is mature and the raw materials are cheap.

[0070] It should be understood that the application of the present invention is not limited to the above examples. For ordinary technicians in this field, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.

Claims

1. A glass-ceramic for temperature measurement, characterized in that: The crystallization temperature of the temperature measuring microcrystalline glass is 400-580°C; in terms of mass percentage, the temperature measuring microcrystalline glass contains: 60-80% silicon dioxide, 10-20% lithium oxide, 3-8% phosphorus pentoxide, 3-10% sodium oxide and potassium oxide, 1-6% aluminum oxide, 1-4% zirconium oxide, 1-5% cerium oxide, and 0.5-3% vanadium compound.

2. The temperature measuring glass-ceramics according to claim 1, characterized in that: The crystallization temperature of the temperature measuring microcrystalline glass is 450-500°C; in terms of mass percentage, the temperature measuring microcrystalline glass includes: 70-75% silicon dioxide, 15-20% lithium oxide, 5-8% phosphorus pentoxide, 6-10% sodium oxide and potassium oxide, 1-4% aluminum oxide, 1-4% zirconium oxide, 1-3% cerium oxide, and 1-2% vanadium compound.

3. A method for preparing the temperature measuring glass-ceramics according to claim 1, characterized in that: include: Obtain glass raw materials, which include, by mass percentage, 60-80% silicon dioxide, 10-20% lithium oxide, 3-8% phosphorus pentoxide, 3-10% sodium oxide and potassium oxide, 1-6% aluminum oxide, 1-4% zirconium oxide, 1-5% cerium oxide, and 0.5-3% vanadium compound; The glass raw materials are melted at a temperature of 1450-1700° C. and subjected to clarification treatment to obtain a glass melt; Casting the molten glass into a shape to obtain a basic glass; The base glass is microcrystallized to obtain the microcrystalline glass for temperature measurement.

4. The method for preparing the temperature measuring glass-ceramics according to claim 3, characterized in that: The obtaining of glass raw materials specifically includes: The silicon dioxide, lithium oxide, phosphorus pentoxide, sodium oxide and potassium oxide, aluminum oxide, zirconium oxide, cerium oxide and vanadium compound are weighed according to the addition ratio, mixed evenly and then ground to obtain the glass raw material, wherein the grinding time is 30-35 minutes and the particle size after grinding is 10-35 microns.

5. The method for preparing the temperature measuring glass-ceramics according to claim 3, characterized in that: The step of melting the glass raw material at a temperature of 1450-1700° C. specifically comprises: The glass raw materials are placed in a crucible, and the crucible is placed in a heating device, and the temperature is increased to 800-1200° C. at a rate of 10-15° C. / min, and then increased to 1450-1700° C. at a rate of 3-5° C. / min, and kept at this temperature for 0.5-5 hours.

6. The method for preparing the temperature measuring glass-ceramics according to claim 3, characterized in that: The step of casting the molten glass into a shape to obtain the basic glass specifically comprises: The molten glass is poured into a preheated mold, and the mold is placed in a muffle furnace heated to 500-520° C. and kept warm for 2.5-3 hours, and then cooled to room temperature to obtain the basic glass.

7. The method for preparing the temperature measuring glass-ceramics according to claim 3, characterized in that: The method of performing microcrystallization treatment on the base glass to obtain the microcrystal glass for temperature measurement specifically includes: The base glass is placed in a heating device, heated to 400-580° C., and kept warm for 2-3 hours to obtain the temperature-measuring microcrystalline glass.

8. The method for preparing the temperature measuring glass-ceramics according to claim 7, characterized in that: The temperature is raised to 400-580° C., wherein the heating rate is 1-5° C. / min.

9. The temperature measuring glass-ceramics according to claim 3, characterized in that: The shape of the temperature measuring glass-ceramic is square or round; the volume of the temperature measuring glass-ceramic is greater than 0.5 cm 3 Less than 2cm 3 .