Method for determining bending deformation of plate glass, glass manufacturing method using same, and glass manufactured using glass manufacturing method

Abstract

The present application relates to a method for determining the bending deformation of plate glass. In the method, the radius of curvature of the plate glass corresponding to the bending deformation of the plate glass is determined on the basis of a Stoney relational expression and / or an elastic-plastic strain relational expression that reflects a configuration for width changes, wherein a first layer and a second layer included in the Stoney relational expression can be set such that, on the basis of a value, obtained by integrating a concentration distribution up to an ion exchange depth layer after ion exchange of glass comprising alkali, and an effective diffusion length, which is the depth calculated to have the same area under the assumption that the surface concentration remains the same according to depth, the thickness corresponding to the effective diffusion length in the thickness of the plate glass is considered as the first layer, and the thickness excluding the effective diffusion length from the thickness of the plate glass is considered as the second layer, and the plastic strain included in the elastic-plastic strain relational expression can be set such that, on the basis of width changes occurring after the ion exchange in the plate glass through a shape change caused by a structural relaxation effect due to a α-relaxation, width changes gradually occurring according to concentration at the ion exchange depth layer are averaged to obtain a single value, the width changes are assumed to occur from the half depth of the ion exchange depth layer to the half depth of a non-ion exchange depth layer through a simple geometric method, and plastic curvature occurs according to the width changes.

Description

Method for determining the amount of bending deformation of plate glass, method for manufacturing glass using the method, and glass manufactured by the method for manufacturing glass

[0001] The present invention relates to a method for manufacturing curved glass with a chemical strengthening effect and an intended curvature, and to chemically strengthened curved glass manufactured by this method. Specifically, the present invention relates to chemically strengthened plate glass with a controlled curvature radius manufactured by a method for determining an ion exchange temperature and a holding time that can implement an arbitrary curvature radius, including cases where the curvature radius has a very large value for a given thickness of plate glass, in order to simultaneously control chemical strengthening performance and the curvature radius.

[0002] Methods for strengthening glass by applying compressive stress to its surface are broadly divided into physical strengthening and chemical strengthening. Chemical strengthening involves replacing alkali ions within the glass with external alkali ions with larger ionic radii through mutual diffusion, thereby applying compressive stress to the surface (Varshneya, Journal of the American Ceramic Society 58 (1975) 106). Chemical strengthening can be applied to glass with even thinner thicknesses than physical strengthening. The demand for chemically strengthened glass is extremely diverse, and its application is expanding beyond the cover windows of existing mobile electronic devices to include automobile window glass and interior display cover windows. For example, ultra-thin glass is being applied to slideable and rollable display modules, including foldable smartphones that utilize flexible display panels, and the application of chemically strengthened glass is expected to continue expanding. Even in the case of general-purpose plate glass, efforts are being made to reduce the thickness of plate glass as a means of reducing greenhouse gas emissions from raw materials and fuels, and in this case, the demand for plate glass processes that apply chemical strengthening methods compared to physical strengthening methods will increase significantly.

[0003] The glass plates subjected to chemical strengthening are broadly categorized into NCS (Na2O-CaO-SiO2) and NAS (Na2O-Al2O3-SiO2) compositions, and these compositions vary widely in detail. Furthermore, depending on the application, not only can the thickness, area, and aspect ratio vary, but the required curvature radius before and after chemical strengthening can also vary. Conventionally, warpage is typically achieved through hot forming, and then ion exchange is performed to maintain the shape while injecting chemical strengthening. Consequently, the ion exchange process conditions are set to maintain the initial warpage. We will now describe specific examples of chemical strengthening for glass plates. For example, an ion exchange process may be required to chemically strengthen flat or curved glass plates while maintaining the curvature radius within an acceptable range. Another example may require a process that significantly changes the curvature radius of a given glass plate by controlling the ion exchange process conditions. The change in the radius of curvature caused by ion exchange in plate glass is influenced by a wide variety of factors. Therefore, up to now, ion exchange conditions that can obtain the desired radius of curvature have been established through a simple, iterative trial and error process. The greatest concern is to secure conditions that prevent additional curvature from occurring during the ion exchange process. In this paper, we present a mathematical formula for the time dependence of the change in radius of curvature of plate glass during the heat treatment for ion exchange, using the mutual diffusion coefficient determined by the composition and ion exchange temperature of the given plate glass and the thickness of the plate glass. By utilizing this relationship, the change in radius of curvature experienced by plate glass with an arbitrary radius of curvature during ion exchange can be determined over time by utilizing the mutual diffusion coefficient according to the thickness and temperature of the plate glass, without simple, iterative trial and error.

[0004] Ion exchange processes for chemical strengthening can be broadly divided into immersion and non-immersion methods. The immersion method, which immerses the glass to be strengthened in a molten alkali salt to cause ion exchange, is commercially applied (Varshneya, International Journal of Applied Glass Science 9(2018) 140). Since this method involves immersing the glass plate in a molten alkali salt, it may actually cause undesirable deformation if ion exchange occurs differently on both sides of the glass plate. Meanwhile, various ion exchange processes can be used to intentionally impart different ion exchange effects depending on the location of the glass plate. In the case of the above-mentioned immersion method, the composition of the molten alkali salt can be formed differently depending on the location of the glass or it can be implemented through masking (Findakly, Optical Engineering 24(1985) 244). In addition, a method of inducing alkali ion migration and diffusion in the thickness direction by applying an electric field in the thickness direction can also be applied (Shaisha, Journal of the American Ceramic Society 64(1981) 278). The non-immersion method is a process in which a slurry or paste containing an alkaline salt is prepared and applied to a glass surface to perform ion exchange in a dry manner. This process facilitates location-selective ion exchange through selective application of the coating, and achieves a desired level of ion exchange by controlling the composition of the coating. Therefore, it may be more effective in imparting different ion exchange effects depending on location than the aforementioned ion exchange methods. Furthermore, various processing methods can be utilized to impart different ion exchange effects depending on the location. For example, differences in the salt composition can lead to differences in the diffusion coefficient, which can in turn lead to differences in not only the compressive stress (CS) but also the depth of layer (DOL).In particular, for other potassium-containing salts except for some KNO3, the DOL can be increased or decreased according to the different diffusion coefficients in glass (Hassani, Journal of Non-Crystalline Solids 515(2019) 143), and for other alkali salts except for K, it has been reported that the CS can be lowered with or without a difference in the diffusion coefficient (Lyu, CeramicsInternational 46(2020) 1697). In the case of the non-immersion method, different ion exchange characteristics can be effectively imparted by controlling the thickness and position of the coating film, the composition of the salt, etc. However, it is known that different ion exchange effects can be imparted by any method or process for performing ion exchange other than the above-mentioned methods.

[0005] Meanwhile, the chemical strengthening properties of plate glass are generally evaluated by surface compressive stress (CS) and depth of layer (DOL). If CS and DOL differ beyond a standard value depending on the location of the plate glass, deformation occurs. In other words, it is a known fact that changes in the radius of curvature of plate glass can occur due to differences in CS and / or DOL applied to both sides. However, until now, the changes in the radius of curvature that occur in response to changes in the thickness of a given plate glass and ion exchange temperature and time have not been quantitatively identified.

[0006] The purpose of this invention is to provide a relationship that can express the size of bending deformation of plate glass occurring during an ion exchange process as a function of the thickness of the plate glass and the ion exchange temperature and time, thereby providing plate glass that is chemically strengthened and has a controlled curvature.

[0007] However, the technical tasks that the embodiments of the present invention seek to achieve are not limited to the technical tasks described above, and other technical tasks may exist.

[0008] According to one embodiment of the present invention, a method for determining a bending deformation amount of plate glass is determined based on a Stoney relationship in a temperature range in which elastic deformation occurs, and a radius of curvature of the plate glass corresponding to the bending deformation amount of the plate glass is determined, wherein the first layer and the second layer included in the Stoney relationship are set to be the first layer, based on an integrated value of a concentration distribution up to an ion-exchange depth layer after ion-exchange of glass including alkali, and an effective diffusion length, which is a depth calculated to have the same area under the assumption that the same surface concentration is the same according to the depth, and a thickness corresponding to the effective diffusion length among the thickness of the plate glass is regarded as the first layer, and a thickness excluding the effective diffusion length among the thickness of the plate glass is regarded as the second layer.

[0009] In addition, the diffusion coefficient in the above Stoney relationship is a value calculated by inversely calculating the diffusion depth (depth of layer) obtained after the ion exchange.

[0010] The above effective diffusion length is a value calculated through parameters set in consideration of the error range that occurs in measuring compressive stress and stress causing bending deformation, and the diffusion depth obtained after the ion exchange.

[0011] In addition, a method for determining the bending deformation of plate glass according to one embodiment of the present invention determines the radius of curvature of the plate glass as a simple sum of viscoelastic curvatures by reflecting the plastic curvature of the plate glass corresponding to the bending deformation of the plate glass based on an elasto-plastic strain-based relationship together with the Stoney relationship in a temperature range where plastic deformation occurs, and the plastic strain included in the elasto-plastic strain-based relationship is based on a width change that appears in the plate glass after ion exchange through a shape change that occurs due to a structural relaxation effect by α-relaxation.

[0012] The above plastic curvature is calculated as a plastic curvature that occurs under the assumption that the width change of the glass up to the ion exchange depth layer after ion exchange including alkali is formed differently depending on the alkali concentration, but the average width change that occurs up to the ion exchange depth layer is constant.

[0013] The above elastomeric strain is a value calculated through a relationship based on the structural relaxation effect caused by α-relaxation, which occurs differently depending on the ion exchange temperature and time during ion exchange.

[0014] The above width change is calculated from the plastic strain among the above elastoplastic strains and the width value of the plate glass. The above width change is a value that gradually changes depending on the concentration from the glass surface (the glass polar surface) to just before the ion exchange layer, and is a value calculated by averaging the width change up to the ion exchange depth layer through integration.

[0015] The above-mentioned ion exchange layer refers to the remaining layer excluding the diffusion depth from the total thickness, i.e., the layer in which ion exchange does not occur.

[0016] The above plastic curvature is a value calculated by assuming that the width change occurs from a thickness change from half the depth of the ion exchange layer to half the depth of the ion exchange layer through a simple geometric method utilizing the above width change.

[0017] In addition, the above viscoelastic curvature is a value calculated as a simple sum of the elastic curvature, which is the bending deformation amount based on the above Stoney relation, and the plastic curvature, which is the bending deformation amount based on the above elastic-plastic strain-based relation.

[0018] In addition, a method for manufacturing glass using the method for determining the bending deformation of plate glass according to the present invention can cause bending deformation corresponding to the radius of curvature in the plate glass through ion exchange of glass including the alkali corresponding to the radius of curvature determined by the method for determining the bending deformation of plate glass.

[0019] In addition, the glass manufactured by the method for manufacturing the glass is a glass manufactured to correspond to a preset relationship between the curvature, compressive stress, effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width change that appears after ion exchange in the plate glass, which is derived based on the Stoney relationship and / or the elastic strain-based relationship that reflects the assumption and the settings for the first layer and the second layer.

[0020] In addition, the glass manufactured by the method for manufacturing the glass is a glass manufactured so that bending deformation occurs corresponding to a predetermined relationship between the curvature, compressive stress, effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width change of the glass, which is derived based on a Stoney relationship in which the assumption and the settings for the first layer and the second layer are reflected, and / or an elastic-plastic strain-based relationship in which the settings for the width change are reflected, in response to ion exchange occurring on a first surface among both sides of the plate glass, and a predetermined relationship between the curvature, compressive stress, effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width change of the glass, which is derived based on a Stoney relationship in which the assumption and the settings for the first layer and the second layer are reflected, and / or an elastic-plastic strain-based relationship in which the settings for the width change are reflected, in response to ion exchange occurring on a second surface among both sides of the plate glass.

[0021] In addition, the glass manufactured by the method for manufacturing the glass is a glass manufactured so that bending deformation occurs corresponding to a predetermined relationship between the curvature, compressive stress, effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width change of the glass, which is derived based on a Stoney relationship in which the assumption and the settings for the first layer and the second layer are reflected, and / or an elastic-plastic strain-based relationship in which the settings for the width change are reflected, in response to ion exchange occurring in a first region among the regions on both sides of the plate glass, and a predetermined relationship between the curvature, compressive stress, effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width change of the glass, which is derived based on a Stoney relationship in which the assumption and the settings for the first layer and the second layer are reflected, and / or an elastic-plastic strain-based relationship in which the settings for the width change are reflected, in response to ion exchange occurring in a second region among the regions on both sides of the plate glass, which is different from the first region.

[0022] When applying ion exchange processes to plate glass, it is essential to understand the warpage distortion that occurs when the CS and DOL values ​​on both sides are different. Despite this, the effects of varying glass thickness and ion exchange temperature and time on the radius of curvature, respectively, have not been quantitatively assessed. Therefore, our research team uses a non-immersion method to form a coating on the cross-section of plate glass, performs heat treatment for ion exchange to induce chemical strengthening, and simultaneously records the deformation of the plate glass in real time to obtain a visual video. Through image analysis, we propose a relationship that relates the magnitude of the warpage distortion induced by ion exchange to the thickness and ion exchange factor of the plate glass. Using this relationship, we can quantitatively infer the warpage distortion corresponding to the ion exchange temperature and holding time based solely on the thickness and temperature-dependent diffusion coefficient of the plate glass. Furthermore, based on this relationship, we can control the radius of curvature of the plate glass by inducing different types of ion exchange on both sides of the plate glass.

[0023] The above-described problem-solving methods are merely exemplary and should not be construed as limiting the present invention. In addition to the exemplary embodiments described above, additional embodiments may be included in the drawings and detailed description of the invention.

[0024] According to an embodiment of the present invention, a relationship is provided that can determine the warpage deformation of a glass plate that occurs through ion exchange in relation to changes in the thickness, mutual diffusion coefficient, alkali concentration distribution, ion exchange temperature, and time of the glass plate.

[0025] In another embodiment of the present invention, a method is provided for intentionally imparting different CS and DOL to a cross-section or both sides of a glass plate having an arbitrary given thickness, particularly through non-immersion ion exchange, and controlling the size of the resulting bending deformation of the glass plate using the above-mentioned relationship, and a glass plate having a controlled curvature is provided through the method.

[0026] Although the examples of this application cover a non-immersion ion exchange case for ease of implementation, the application is possible for various ion exchange methods, and the examples are merely exemplary and should not be construed as limiting the present application.

[0027] In addition to the exemplary embodiments described above, additional embodiments may exist in the drawings and detailed description of the invention.

[0028] However, the effects that can be obtained from this center are not limited to the effects described above, and other effects may exist.

[0029] Figure 1 is a modified version of a concentration distribution graph by general diffusion.

[0030] Figure 2 shows the concentration distribution and effective diffusion length for the glass depth.

[0031] Figure 3 shows the stress distribution and effective stress for the glass depth.

[0032] Figure 4 is an example of various strain distributions caused by stress after ion exchange.

[0033] Figure 5 is a schematic diagram of the change in curvature caused by a change in width.

[0034] Figure 6 is a photograph of glass that has undergone deformation after ion exchange at different temperatures.

[0035] Figure 7 is a graph showing the real-time temperature measurement and glass deformation during heat treatment at 440°C for 15 minutes.

[0036] Figure 8 is a graph of the amount of glass deformation measured in real time according to ion exchange temperature.

[0037] Figure 9 is a graph of the deformation rate of glass measured in real time according to ion exchange temperature.

[0038] Figure 10 is a graph of glass curvature measured in real time according to ion exchange temperature.

[0039] Figure 11 shows the temperature-dependent diffusion coefficient of sodium alumino-silicate glass.

[0040] Figure 12 shows the calculation of the effective diffusion length according to the virtual ion exchange time.

[0041] Figure 13 shows the relevant indices of glass used in calculating the relational expression.

[0042] Figure 14 shows the σ0 value used in the calculation according to ion exchange temperature.

[0043] Figure 15 (a) shows the change in curvature over time when CS is a constant σ0 for each ion exchange temperature, and (b) shows the change in curvature over time for each actual ion exchange temperature.

[0044] Figure 16 shows the curvature strain over time of a cross-sectional ion-exchange glass at 425°C for 15 minutes, the behavior of the curvature strain calculated by the measured CS, and the behavior of the fitting equation.

[0045] Figure 17 shows the change in curvature strain fitting CS according to α at each temperature.

[0046] Figure 18 shows the CS measurements used for ion exchange temperature and time-dependent calculations.

[0047] Figure 19 (a) shows the change in curvature over time (line) when CS is σ0 for each ion exchange temperature and the curvature (symbol) calculated with the measured CS, and (b) shows the change in curvature over time for each actual ion exchange temperature.

[0048] Figure 20 shows the expected curvature change over time at different ion exchange temperatures.

[0049] Figure 21 shows the expected curvature change over time for each CS at a temperature of 425°C.

[0050] Figure 22 shows the expected curvature change according to DOL for each CS at a temperature of 425°C.

[0051] Figure 23 shows the CS, DOL, and curvature measurement values ​​for each ion exchange condition used in calculating the effective diffusion length.

[0052] Figure 24 shows the effective film thickness (x-axis) calculated using the Stoney relation and the effective diffusion length (y-axis) calculated from the concentration distribution.

[0053] Figure 25 shows the distribution of alkali ion concentration along the depth measured by SEM-EDS for a cross-section of a 7-minute cross-section ion-exchange glass at 425°C.

[0054] Figure 26 compares the optical DOL measured by FSM and the chemical DOL measured by SEM-EDS.

[0055] Figure 27 shows a comparison of the effective diffusion length obtained from the concentration distribution area and the effective diffusion length calculated as a constant multiple of the optically measured DOL.

[0056] Figure 28 shows the CS, DOL, and curvature measurement values ​​for each ion exchange condition used in calculating the effective stress.

[0057] Figure 29 shows the effective stress (x-axis) calculated from the stress distribution obtained from the concentration distribution and the stress (y-axis) calculated using the Stoney relation of mathematical expression 7.

[0058] Figure 30 shows a comparison of the effective stress obtained by area and the effective stress calculated as a constant multiple of the optically measured stress when the concentration distribution is assumed to be the same as the stress distribution.

[0059] Figure 31 shows the heat treatment conditions and CS / DOL of the air / tin side of general float glass. Journal of the Australian Ceramic Society 57 (2021) 1331).

[0060] Figure 32 shows the amount of bending deformation according to the length of the glass.

[0061] Figure 33 shows the diffusion coefficients of the air and tin sides of a typical float glass ( Journal of the Australian Ceramic Society 57(2021) 1331).

[0062] Figure 34 shows the change in curvature over time obtained under heat treatment conditions at 425°C for 8 hours.

[0063] Figure 35 shows the deformation control of general float glass under ion exchange conditions at 435°C for 12 hours.

[0064] Figure 36 shows the conditions for non-deformation and the difference in curvature radius of the air / tin side in general float glass.

[0065] Figure 37 shows the relevant parameters of soda-lime silicate glass used in stress calculations (Macrelli, International Journal of Applied Glass Science 11 (2020) 730).

[0066] Figure 38 shows the calculated values ​​of CS according to changes in thickness and DOL.

[0067] Figure 39 shows the CS change due to DOL and thickness change.

[0068] Figure 40 is a graph of the amount of glass deformation measured in real time according to ion exchange temperature.

[0069] Figure 41 is a graph of the deformation rate of glass measured in real time according to ion exchange temperature.

[0070] Figure 42 shows the relevant indices of glass used in calculating the relational expression.

[0071] Figure 43 shows the CS, DOL, and curvature measurement values ​​used in calculations according to ion exchange temperature conditions.

[0072] Figure 44 is a graph of glass curvature measured in real time according to ion exchange temperature.

[0073] Figure 45 is a graph of the glass plasticity curvature measured in real time according to the ion exchange temperature.

[0074] Figure 46 is a graph comparing the calculated plastic curvature and the actual curvature according to ion exchange conditions.

[0075] Figure 47 is a photograph of a glass that was deformed after ion exchange at different temperatures using LiNO3 slurry.

[0076] Figure 48 is a graph of the curvature of glass measured in real time according to ion exchange temperature.

[0077] Below, with reference to the attached drawings, an embodiment of the present invention is described in detail so that a person having ordinary knowledge in the technical field to which the present invention pertains can easily carry out the present invention.

[0078] However, the present invention can be implemented in various different forms and is not limited to the embodiments described herein. In order to clearly explain the present invention in the drawings, parts irrelevant to the description have been omitted, and similar parts have been designated with similar drawing reference numerals throughout the specification.

[0079] Throughout this specification, when a part is said to be "connected" to another part, this includes not only cases where it is "directly connected" but also cases where it is "electrically connected" with another element in between.

[0080] Throughout this specification, when it is said that a member is located “on,” “above,” “upper,” “lower,” “lower” or “lower” another member, this includes not only cases where the member is in contact with the other member, but also cases where another member exists between the two members.

[0081] Throughout this specification, whenever a part is said to "include" a component, this does not mean that it excludes other components, but rather that it may include other components, unless otherwise specifically stated.

[0082] Hereinafter, a method for determining the amount of bending deformation of plate glass according to one embodiment of the present invention, a method for manufacturing glass according to the determination method, and glass are described.

[0083] The method for determining the amount of warpage deformation of plate glass according to the present invention determines the radius of curvature of the plate glass corresponding to the amount of warpage deformation of the plate glass based on the Stoney relation and / or the elastic-plastic strain-based relation, wherein the first layer and the second layer included in the Stoney relation are set to be the first layer only, based on the integrated value of the concentration distribution up to the ion-exchange depth layer after ion-exchange of glass including alkali, and the effective diffusion length, which is the depth calculated to have the same area under the assumption that the same surface concentration is the same according to the depth, and the thickness of the plate glass excluding the effective diffusion length is set to be the second layer only, and the plastic strain included in the elastic-plastic strain relation is based on the width change that appears after ion-exchange in the plate glass through the shape change caused by the structural relaxation effect by α-relaxation, and the width change that gradually changes according to the concentration in the ion-exchange depth layer is averaged and reported as one value, and the plastic strain included in the elastic-plastic strain relation is determined by a simple geometric method from half the depth of the ion-exchange depth layer to the non-ion-exchange depth layer. It is assumed that the width change occurs up to half the depth of the depth layer, and it is set that the plastic curvature occurs according to the width change. Here, the diffusion coefficient in the Stoney relation is a value calculated by inversely calculating the depth of layer obtained after the ion exchange. In addition, the effective diffusion length is a value calculated through parameters set in consideration of the error range that occurs for the measurement of compressive stress and the stress that causes bending deformation, and the diffusion depth obtained after the ion exchange. In addition, the plastic strain in the elastic-plastic strain-based relation is a value calculated from parameters set in consideration of the shape change that occurs due to structural relaxation, which is α-relaxation, and the concentration distribution of alkali. In addition, the width change is a value calculated through parameters set in accordance with the assumption and the plastic strain.

[0084] More specifically, the method for determining the amount of warpage deformation of plate glass according to one embodiment of the present invention determines the radius of curvature of the plate glass corresponding to the amount of warpage deformation of the plate glass based on the Stoney relation in a temperature range in which elastic deformation occurs, wherein the first layer and the second layer included in the Stoney relation are a value obtained by integrating the concentration distribution up to the ion exchange depth layer after ion exchange of glass including alkali, and an effective diffusion length, which is a depth calculated to have the same area under the assumption that the same surface concentration is the same according to the depth, and a thickness corresponding to the effective diffusion length depth among the thickness of the plate glass may be set to be regarded as the first layer, and a thickness excluding the effective diffusion length depth among the thickness of the plate glass may be regarded as the second layer.

[0085] Meanwhile, a method for determining the bending deformation of plate glass according to one embodiment of the present invention determines the radius of curvature of the plate glass by a simple sum of viscoelastic curvatures by reflecting the plastic curvature of the plate glass corresponding to the bending deformation of the plate glass based on an elasto-plastic strain-based relation together with the Stoney relation in a temperature range where plastic deformation occurs, and the plastic deformation included in the elasto-plastic strain-based relation may be based on a width change that appears in the plate glass after ion exchange through a shape change caused by a structural relaxation effect due to -relaxation.

[0086] In addition, the above plastic curvature can be calculated as a plastic curvature that occurs under the assumption that the average width change that occurs up to the ion exchange depth layer is constant up to the ion exchange depth layer.

[0087] In addition, the above-mentioned elastomeric strain may be a value calculated through a relationship based on the structural relaxation effect caused by α-relaxation that occurs differently depending on the ion exchange temperature and time during ion exchange.

[0088] In addition, the above width change is calculated from the plastic strain among the elastic strains and the width value of the plate glass, and may be a value that changes according to the concentration from the glass surface to just before the ion exchange layer, and may be a value calculated by averaging the width change up to the ion exchange depth layer through integration.

[0089] In addition, the above plastic curvature may be a value calculated by assuming that the width change occurred in a thickness change from half the depth of the non-ion exchange layer to half the depth of the ion exchange depth layer through a simple geometric method utilizing the width change.

[0090] In addition, the viscoelastic curvature may be a value calculated as a simple sum of the elastic curvature, which is a bending deformation amount based on the Stoney relation, and the plastic curvature, which is a bending deformation amount based on the elastic-plastic strain-based relation.

[0091] Meanwhile, a method for manufacturing glass using a method for determining a bending deformation amount of plate glass according to the present invention can cause a bending deformation corresponding to a radius of curvature in the plate glass through ion exchange of glass containing the alkali corresponding to the radius of curvature determined by the method for determining a bending deformation amount of plate glass.

[0092] In addition, the glass manufactured by the method for manufacturing the glass is glass manufactured to correspond to a preset relationship among the curvature, compressive stress, effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width of the glass derived based on a Stoney relationship that reflects the above assumptions and settings for the first layer and the second layer and / or an elastic strain-based relationship that reflects settings for the width change.

[0093] More specifically, the glass can be manufactured so that, in a temperature range where elastic deformation occurs, bending deformation occurs corresponding to a preset relationship between the curvature, compressive stress, and effective diffusion length of the glass derived based on the Stoney relationship that reflects the assumption and the settings for the first layer and the second layer.

[0094] Meanwhile, the glass can be manufactured to correspond to a preset relationship between the curvature, compressive stress, effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width change that appears after ion exchange in the plate glass, which are derived based on an elasto-plastic strain-based relationship together with the Stoney relationship in a temperature range where plastic deformation occurs.

[0095] In addition, according to one embodiment of the present invention, the glass manufactured by the method for manufacturing the glass may be a glass manufactured such that a bending deformation occurs corresponding to a preset relationship among curvature, compressive stress, effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width of the glass derived based on a Stoney relationship in which the assumption and settings for the first layer and the second layer are reflected, and / or an elastic-plastic strain-based relationship in which the setting for the width change is reflected, in response to ion exchange occurring on a first surface among both sides of the plate glass, and a preset relationship among curvature, compressive stress, effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width of the glass derived based on a Stoney relationship in which the assumption and settings for the first layer and the second layer are reflected, and / or an elastic-plastic strain-based relationship in which the setting for the width change is reflected, in response to ion exchange occurring on a second surface among both sides of the plate glass.

[0096] More specifically, the glass can be manufactured so that, in a temperature range where elastic deformation occurs, bending deformation occurs corresponding to a predetermined relationship between the curvature, compressive stress, and effective diffusion length of the glass derived based on a Stoney relationship that reflects the assumption and the settings for the first layer and the second layer in response to ion exchange occurring on a first side among the two sides of the plate glass, and a predetermined relationship between the curvature, compressive stress, and effective diffusion length of the glass derived based on a Stoney relationship that reflects the assumption and the settings for the first layer and the second layer in response to ion exchange occurring on a second side among the two sides of the plate glass.

[0097] Meanwhile, the glass may be manufactured so that, in a temperature range where plastic deformation occurs, bending deformation occurs corresponding to a predetermined relationship between the curvature, compressive stress, and effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width of the glass, which is derived based on an elastic-plastic strain-based relationship in which a setting for a width change that appears in the glass after ion exchange is reflected, together with a Stoney relationship in which the assumption and the settings for the first and second layers are reflected, in response to ion exchange occurring on the first side of the two sides of the glass, and a predetermined relationship between the curvature, compressive stress, and effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width of the glass, which is derived based on an elastic-plastic strain-based relationship in which a setting for a width change is reflected, together with a Stoney relationship in which the assumption and the settings for the first and second layers are reflected, in response to ion exchange occurring on the second side of the two sides of the glass.

[0098] The temperature range in which the above plastic deformation occurs may be a temperature range in which elastic-plastic deformation occurs, in which plastic deformation occurs together with the above elastic deformation.

[0099] Such glass can be manufactured by a method of controlling the curvature of the plate glass by controlling the amount of deformation due to ion exchange occurring on the first side (one side) and the amount of deformation due to ion exchange occurring on the second side (the other side) of the two sides of the plate glass. For example, the glass manufactured in this way can be manufactured as glass characterized in that different ion exchanges are imparted to both sides by being manufactured according to a method of controlling the curvature of the plate glass.

[0100] In addition, according to one embodiment of the present invention, the glass manufactured by the method for manufacturing the glass may be a glass manufactured so that a bending deformation occurs corresponding to a preset relationship among curvature, compressive stress, effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width of the glass, which is derived based on a Stoney relationship in which the assumption and the settings for the first layer and the second layer are reflected, and / or an elastic-plastic strain-based relationship in which the settings for the width change are reflected, in response to ion exchange occurring in a first region among the regions on both sides of the plate glass, and a preset relationship among curvature, compressive stress, effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width of the glass, which is derived based on a Stoney relationship in which the assumption and the settings for the first layer and the second layer are reflected, and / or an elastic-plastic strain-based relationship in which the settings for the width change are reflected, in response to ion exchange occurring in a second region among the regions on both sides of the plate glass, different from the first region.

[0101] More specifically, the glass can be manufactured so that, in a temperature range where elastic deformation occurs, bending deformation occurs corresponding to a preset relationship between the curvature, compressive stress, and effective diffusion length of the glass derived based on a Stoney relationship that reflects the assumption and the settings for the first layer and the second layer in response to ion exchange occurring in a first region among the regions on both sides of the plate glass, and a preset relationship between the curvature, compressive stress, and effective diffusion length of the glass derived based on a Stoney relationship that reflects the assumption and the settings for the first layer and the second layer in response to ion exchange occurring in a second region different from the first region among the regions on both sides of the plate glass.

[0102] Meanwhile, the glass may be manufactured so that, in a temperature range where plastic deformation occurs, a bending deformation occurs corresponding to a predetermined relationship between the curvature, compressive stress, and effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width of the glass, which is derived based on an elasto-plastic strain-based relationship in which a setting for a width change that appears after ion exchange in the glass is reflected, together with a Stoney relationship in which the assumption and the settings for the first and second layers are reflected, in response to ion exchange occurring in a first region among the regions on both sides of the glass, and a predetermined relationship between the curvature, compressive stress, and effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width of the glass, which is derived based on an elasto-plastic strain-based relationship in which a setting for a width change that appears after ion exchange in the glass is reflected, together with a Stoney relationship in which the assumption and the settings for the first and second layers are reflected, in response to ion exchange occurring in a second region among the regions on both sides of the glass, different from the first region.

[0103] Here, the first region and the second region may be regions located on the same side of both surfaces of the plate glass (for example, the first region is located on the first side and the second region is located on the second side, or conversely, the first region is located on the second side and the second region is located on the first side), or may be regions located on different sides (for example, both the first region and the second region are located on the first side, or both the first region and the second region are located on the second side).

[0104] That is, the glass manufactured by the method for manufacturing the glass can be manufactured by individually applying ion exchange to a plurality of regions including the first region and the second region. For example, different ion exchanges can be applied to at least some of the plurality of regions, thereby inducing different bending deformations in at least some of the regions.

[0105] By applying ion exchange individually to multiple areas of the plate glass in this way, plate glass having one or more curvatures can be manufactured so that the curvature and compressive stress or strengthening depth or alkali ion concentration distribution of each area have characteristics corresponding to the corresponding bending deformation.

[0106] In addition, the present invention provides a relationship that can quantitatively determine the amount of warpage of alkali-containing silicate glass plate having a flat surface by utilizing the compressive or tensile stress and diffusion depth generated at the glass surface through ion exchange, thereby providing a curved glass plate with controlled warpage deformation while being chemically strengthened. The relationship is based on the Stoney relationship applied under other conditions and / or an elasto-plastic strain-based relationship that reflects the setting for the above width change, and is modified to be suitable for glass plate undergoing ion exchange, so that the warpage deformation according to the ion exchange temperature and time can be quantitatively determined only with the thickness and diffusion coefficient of the glass plate given through calculation. Various examples were implemented to show that the warpage deformation of the glass plate can be controlled by utilizing the relationship proposed in the present invention. Specifically, a non-immersion ion exchange method that facilitates location-selective ion exchange can be applied, and a slurry containing an alkali salt such as KNO3, LiNO3, a solvent for the alkali salt such as water, and a metal oxide can be utilized, and in addition, a viscosity modifier can be added, and by controlling the components in the slurry (e.g., the content ratio between the alkali salt, the solvent, and the metal oxide, etc.), different ion exchange effects can be imparted to both sides of the plate glass, and accordingly, the radius of curvature of the plate glass according to the ion exchange conditions can be controlled by utilizing the corresponding relationship, and a curved glass with controlled curvature having such characteristics can be produced.

[0107] It is well known that warpage occurs when the difference in the magnitude of stress generated after ion exchange on both sides of plate glass and / or the depth at which the stress exists exceeds a standard value. However, to date, the quantitative correlation between the warpage deformation according to conditions such as the thickness of the plate glass, diffusion coefficient, ion exchange temperature, and time has not been analyzed. In the present invention, a relationship is proposed that can quantitatively determine the magnitude of the bending deformation of the plate glass at any temperature and time by utilizing the thickness of the plate glass and the diffusion coefficient of the alkali ion participating in the ion exchange, and by utilizing the relationship, the plate glass is characterized by being chemically strengthened while having a controlled curvature.

[0108] Chemical strengthening is continuously expanding its application areas, encompassing not only the cover windows of existing mobile electronic devices, but also automotive glass, pharmaceutical glass, and even ultra-thin glass used in flexible display modules such as foldable, slideable, and rollable displays. Recently, efforts are being made to reduce the thickness of general-purpose plate glass to achieve carbon neutrality. Consequently, chemical strengthening, which is only applicable to thin glass, will be adopted, further increasing the demand for chemical strengthening processes. Currently, plate glass has a wide range of properties, such as composition, thickness, and area, depending on the application. Depending on the application, various ion exchange processes are expected to be required, such as strengthening flat glass while maintaining its flat state, strengthening while imparting bending deformation, or strengthening curved glass without deformation. Therefore, by providing a relationship for the amount of bending deformation caused by ion exchange in plate glass, the radius of curvature can be quantitatively inferred according to conditions such as the diffusion coefficient of plate glass, ion exchange temperature, and time, and further, by imparting different ion exchange effects to both sides of plate glass, curved glass with a controlled radius of curvature can be provided, thereby omitting or simplifying the curved forming step.

[0109] This invention provides a relationship for calculating the radius of curvature for warpage deformation that occurs in silicate-based plate glass containing alkali ions, depending on the glass' thickness, diffusion coefficient, shape, ion exchange temperature, and time. This relationship allows for the creation of curved glass capable of quantitatively controlling the radius of curvature that occurs before and after ion exchange, such as maintaining, increasing, or decreasing the curvature after ion exchange. Furthermore, to control the radius of curvature, different ion exchange effects can be imparted to both sides of the plate glass, and a non-immersion ion exchange method can be utilized for this purpose. To achieve this, an alkali salt such as KNO3 or LiNO3 is mixed with a solvent such as water and metal oxide particles to create a slurry, which is then applied to the glass surface and heat-treated to induce ion exchange. By controlling the mixing ratio of the slurry components, different ion exchange characteristics are exhibited at different locations selectively, thereby controlling the warpage deformation of the plate glass. Through this, the present invention provides curved glass characterized by simultaneous control of chemical strengthening and warpage deformation.

[0110] In this application, we propose a mathematical formula as a method for controlling the above-mentioned warpage deformation, and utilize this formula to implement a process for inducing ion exchange on one or both sides of plate glass. To achieve this, a mathematical formula is required that expresses the radius of curvature that occurs in the plate glass with respect to the temperature and time of the ion exchange heat treatment step. In order to devise a mathematical formula that is useful at both an engineering and practical level, we observed the warpage deformation of plate glass caused by ion exchange in real time and analyzed it numerically. Furthermore, we present the main idea implied by the mathematical formula in the claims. This starts from a novel setting that divides the exchanged layer, where ion exchange occurs, and the non-exchanged layer, where ion exchange does not occur, into two layers with different physical properties in elastic deformation. That is, the thickness of each layer changes with a certain correlation as ion exchange progresses, and the key is to numerically relate this to the change in the radius of curvature. The Stoney equation is a method to calculate the compressive or tensile stress applied to two sheets of material with different coefficients of thermal expansion or other properties by relating the radius of curvature of the sheets to the thickness of each sheet when the two sheets are physically or chemically bonded with a level of strength that does not cause the interface to delaminate. As an example of a representative case where the Stoney equation is well applied, when bending deformation occurs due to the difference in properties between a silicon wafer substrate and a thin film formed by deposition or oxidation in the field of semiconductor device processing, the compressive or tensile stress that occurs elastically can be calculated by substituting the radius of curvature and the thickness of each layer, and it can be usually expressed by the following mathematical equation 1 (Stoney, Proceedings of the Royal Society of London A 82(1909) 172).

[0111] [Mathematical Formula 1]

[0112]

[0113] In the above mathematical expression 1, σ is the stress generated between the film and the substrate, E is the Young's modulus of the substrate, v s is the Poisson's ratio of the substrate, h s and h f are the thickness of the substrate and film, respectively, and R represents the radius of curvature corresponding to the bending deformation. In addition, h is obtained through mathematical expression 1. s h on a substrate having a thickness of f The stress σ that occurs between the substrate and the film can be calculated by measuring the radius of curvature R of the bending deformation that occurs when a film having a thickness of is formed.

[0114] In this study, the above mathematical formula 1 was applied to plate glass in which ion exchange occurs, and it was confirmed that this idea has not been reported at all in previous reports. That is, if the DOL layer corresponding to the exchange layer where ions diffused into the plate glass through ion exchange are distributed is set as a film, and the non-exchanged layer in which ion exchange does not occur is set as a substrate, and then the compressive or tensile stress is replaced by CS, the following mathematical formula 2 can be obtained.

[0115] [Equation 2]

[0116]

[0117] In the above mathematical expression 2, d glassis the total thickness of the plate glass where ion exchange is performed, and it is assumed that DOL has a value less than half of the total thickness of the plate glass. In order for the thickness of the DOL layer inserted in mathematical equation 2 to be applied to Stoney's relation, the exchange layer must have a uniform composition and the physical properties such as Poisson's ratio and Young's modulus must be maintained the same within the thickness of the film (i.e., the thickness of the exchange layer). However, it is a well-known fact that ion exchange occurs by mutual diffusion, and the distribution of ion-exchanged ions within the DOL layer is not constant. Therefore, it is necessary to solve the problem related to the applicability of Stoney's relation, which occurs because the concentration of the invading ion decreases gradually as the diffusion depth from the surface increases. Meanwhile, the concentration distribution of alkali ions diffused into the glass is generally expressed by the following mathematical equation 3 (Sun, International Journal of Applied Glass Science 11(2020) 134).

[0118] [Equation 3]

[0119]

[0120] Here, C(x,t) represents the concentration at the depth x from the surface where ion exchange occurs and the time t where ion exchange occurs, C0 represents the concentration of the corresponding alkali ion present in the plate glass before ion exchange, A represents a constant, and D represents the diffusion coefficient corresponding to the corresponding mutual diffusion.

[0121] Figure 1 is a modified version of a concentration distribution graph by general diffusion.

[0122] Fig. 1 is a graph showing the concentration distribution that occurs when C0 = 0 and A = 1 are assumed for mathematical expression 3. The concentration distribution graph may have different shapes depending on time, and as the depth increases from the glass surface, the concentration of the intruded alkali ions gradually converges to 0. At this time, the concentration of alkali ions at the extreme surface where the depth is x = 0 has the largest value, C(0, t), and the depth at which the actual measured concentration of the intruded alkali ions becomes 0 can be defined as the diffusion depth (chemical DOL) in the concentration distribution. At this time, the total amount of ion-exchanged alkali ions can be quantitatively determined by calculating the area corresponding to the integral in the shape of Fig. 1. In addition, the diffusion coefficient D can be approximated through inverse calculation from the diffusion depth obtained after ion exchange, and can be expressed in a simplified form by the following mathematical expression 4.

[0123] [Equation 4]

[0124]

[0125] As described above, in the graph of Fig. 1, the area represents the total amount of alkali ions that have invaded, and the thickness at which the total amount is maintained constant at the concentration of C(0,t) at the extreme surface where the maximum stress occurs can be assumed, and this is given as the newly given effective diffusion length (d). eff ) is to be defined. By utilizing the effective diffusion length, the concentration of alkali ions within the effective diffusion length is equal to the concentration at the polar surface, so the factor can be directly applied to the Stoney relation.

[0126] Figure 2 shows the concentration distribution and effective diffusion length for the glass depth.

[0127] Figure 2 schematically illustrates the effective diffusion length that can be defined from the concentration distribution. The effective diffusion length can be determined by calculating the distance at which the red area, which represents the total amount of alkali ions that have penetrated, and the blue area, which has the same concentration as the initial concentration C(0,t) at the polar surface, become equal. In other words, the effective diffusion length corresponding to the thickness of the uniform exchange layer having the concentration at the polar surface can be defined from the blue area that becomes equal to the red area. The effective diffusion length can be expressed by the following mathematical equation (5), and when the concentration distribution is expressed in the form of a margin of error function as in mathematical equation (3), it corresponds to 0.514 times the DOL. It is a matter of course that the effective diffusion length can be derived by calculating the area using a numerical analysis method even in situations where the concentration distribution is not expressed in the form of a margin of error function.

[0128] [Equation 5]

[0129]

[0130] Here, DOL can be corresponded to the diffusion depth measured by an optical method such as a surface stress meter (FSM) (optical DOL, hereinafter collectively referred to as 'DOL').

[0131] It is a well-known fact that even in situations where the concentration distribution is not expressed in the form of a variance function, the effective diffusion length can be derived by calculating the area using numerical analysis methods. In this case, the effective diffusion length can be expressed as in Equation 6.

[0132] [Equation 6]

[0133]

[0134] In mathematical expression 6, α is a parameter with a value between 0 and 1. The corresponding α value can be set to a constant value when the actual integral area is the same, and additionally, the value can fluctuate in consideration of the error range that occurs in the measurement of CS and the stress that causes the actual bending deformation.

[0135] Using Equation 5, the diffusion depth obtained from the concentration distribution can be converted into an effective diffusion length. Consequently, the equation can be utilized by distinguishing between a film layer (or exchange layer) and a substrate layer (or non-exchange layer) having a uniform composition that satisfies the application conditions of the Stoney relation. Accordingly, the bending deformation in ion-exchanged glass can be expressed as follows.

[0136] [Equation 7]

[0137]

[0138] At this time, if mathematical expressions 4 and 5 are used under the assumption that the concentration distribution follows the error function, mathematical expression 8 is ultimately derived.

[0139] [Equation 8]

[0140]

[0141] Therefore, Equation 8 includes the ion exchange time and diffusion coefficient assuming elastic deformation, and since the temperature dependence of the diffusion coefficient corresponding to ion exchange occurring in glass is already well known in the field, Equation 8 relates the radius of curvature and stress of the corresponding plate glass according to the ion exchange time and temperature.

[0142] While Equation 8 addresses the case where ion exchange occurs on only one side of the glass, it can also address the more general case where ion exchange occurs on both sides of the glass. That is, the CS and / or DOL may or may not be formed differently on both sides of the glass, resulting in curvature. In such cases, the resulting radius of curvature due to the difference in curvature on each side of the glass can be expressed by Equation 9 below.

[0143] [Equation 9]

[0144]

[0145] In the above mathematical expression 9, the subscripts 1 and 2 each represent one side of the corresponding plate glass.

[0146] For example, if CS and DOL on both sides of the glass plate are the same as in mathematical equation 8, no warpage deformation will occur, and even if CS and DOL on both sides are formed differently, the overall size of the warpage deformation of the glass plate can be determined. That is, in order to intentionally induce warpage deformation, CS or DOL applied to each side can be made different. As a specific example, CS or DOL can be formed differently by applying different glass plate thickness, coating thickness, composition within the coating, and heat treatment conditions by applying a dry ion exchange process.

[0147] In one or more embodiments, mathematical expression 7 or mathematical expression 9 may be utilized, and the magnitude of the bending deformation, DOL, and CS occurring during single-sided or double-sided ion exchange may be determined through the corresponding relationship.

[0148] CS has a variable value that varies depending on various factors such as time, temperature, and glass type. Many studies have been conducted to infer CS, and a representative calculation formula exists that can infer CS from the concentration distribution (Sane, Journal of the American Ceramic Society 70 (1987) 86). A more recently proposed calculation formula also includes the stress relaxation effect that occurs during the ion exchange process and is expressed as Equation 10 (Macrelli, Journal of Non-Crystalline Solids 522 (2019) 119457).

[0149] [Equation 10]

[0150]

[0151] In Equation 10, B is the linear network dilation coefficient (LNDC), E is Young's modulus, v is Poisson's ratio, C(x,t) is the concentration of exchanged ions at an arbitrary depth x and ion exchange time t, C * (t) is the total average concentration of exchanged ions at any time t, and R(t) represents the stress relaxation effect over time. B can be expressed by the following mathematical equation (11).

[0152] [Equation 11]

[0153]

[0154] In mathematical expression 11, V represents the volume of the glass where ion exchange occurs. The change in the volume of the glass due to the total amount of ions introduced by the introduction of B can be calculated, and thus the compressive stress caused by the introduced ions can be calculated.

[0155] Also, when it is assumed that there is no stress relaxation effect in Equation 10, the stress can be expressed in a simplified form as in Equation 12.

[0156] [Equation 12]

[0157]

[0158] In some embodiments, it can be confirmed that the stress distribution obtained from the concentration distribution can be calculated using Equation 10 or 12, and consequently, σ(0, t), which represents the surface compressive stress, can also be calculated. The CS obtained through such calculations can be utilized in Equation 7 or 9.

[0159] In some embodiments, CS can be considered a constant σ0. That is, compared to DOL, CS varies less under given ion exchange conditions and contributes less to the final radius of curvature change in Equation 8, so it can be considered a constant. Here, the CS considered as a constant can be the surface compressive stress measured by an optical measuring device after ion exchange has proceeded at an appropriate ion exchange temperature and time. Therefore, the CS measured after ion exchange can be utilized as a constant term in Equation 8.

[0160] Figure 3 shows the stress distribution and effective stress for the glass depth.

[0161] Figure 3 schematically represents the effective stress that can be defined from the stress distribution.

[0162] In some embodiments, CS is the effective stress (CS eff ) can be considered. In the CS used in the Stoney relation, it is easy to infer that the stress representing the deformation in the actual Stoney relation is not the same as the CS generated after ion exchange. Therefore, the effective stress can be determined by finding the stress at which the red area, which means the actual stress amount up to the effective diffusion length defined above in the stress distribution, and the blue area having the same stress at the effective diffusion length become equal. In other words, it can be defined as a single layer having the same stress from the blue area equal to the red area to the effective diffusion length. The effective stress can be expressed by the following mathematical expression 13, and since it is possible to assume that the stress distribution simply follows the concentration distribution, if the concentration distribution is expressed in the form of a margin of error function as in mathematical expression 3, the CS, which is the compressive stress measured by an optical method such as a surface stress meter (FSM) mea It corresponds to 0.722 times. It is a natural fact that the effective stress can be derived by calculating the area using a numerical analysis method even in a situation where the concentration distribution is not expressed in the form of a margin of error function.

[0163] [Equation 13]

[0164]

[0165] However, when the ion exchange temperature is excessively high or the ion exchange time is excessively long, the stress relaxation effect may occur significantly, which may cause plastic deformation, and CS may not be maintained as a constant but may excessively show a tendency to decrease. Therefore, the range of suitable conditions in which CS can be utilized as an effective stress in the Stoney relation based on elastic behavior is, for example, an ion exchange temperature of less than 600°C and a DOL of 15 μm or less, and preferably, the ion exchange temperature may be set to 500°C or less and a DOL of 10 μm or less, but in other conditions, mathematical expression 8 may be utilized by substituting the effective stress derived from the measured CS value.

[0166] This paper also defines plastic deformation, which deviates from the elastic deformation based on the Stoney relation mentioned above. In addition to the mathematical equation for the final elastic deformation, it provides a mathematical equation for additional deformation that occurs plastically. As previously mentioned, when the ion exchange temperature is excessively high or the ion exchange time is excessively long, the stress relaxation effect occurs significantly, resulting in plastic deformation. This causes a discrepancy between the mathematical equation based on the Stoney relation defined herein and the actual values. While ion exchange is known to occur elastically, the structural relaxation effect caused by α-relaxation not only reduces stress due to changes in elasto-plastic strain but also causes additional shape changes. In small cases, only stress decreases, or plastic curvature occurs in addition to the reduced stress, allowing the calculation of deformation with stress. In extreme cases, this paper can also be applied to cases where only plastic deformation occurs, resulting in the absence of stress and only plastic deformation. In particular, in processes such as forming curved glass where plastic deformation is applied, a method has been used to apply plastic deformation to the glass without stress by utilizing a mold having a specific amount of bending deformation and applying pressure. However, if the mathematical formula for calculating plastic deformation provided in this invention is applied industrially, glass with a curved shape that is intentionally applied with a small amount of stress or in a stress-free plastic deformation situation can be easily obtained through an ion exchange process without a mold. This invention utilizes a previously known stress calculation formula to calculate plastic deformation caused by chemical strengthening. Attempts to calculate stress caused by chemical strengthening have been continuously made, and thus a formula for calculating stress caused by α-relaxation that occurs plastically already exists.However, all of these equations were designed for the purpose of comparison with actual stresses and assume full ion exchange, and it was confirmed that there is no attempt to calculate the partial or full deformation amount due to shape change caused by actual α-relaxation.

[0167] Figure 4 shows various strain distributions caused by stress after ion exchange.

[0168] Figure 4 shows various strain distributions that occur after ion exchange, which are known to exist. The chemical strengthening method by ion exchange can generate various strain distributions depending on the assumption (Varshneya, International Journal of Applied Glass Science 1 (2010) 131). The strain distribution when the stress generated only in the ion exchange depth layer after ion exchange is perfectly elastic is expressed as ε C It can be defined as , and can be expressed by mathematical formula 14. At this time, since the strain change occurs in the entire area due to the concentration distribution existing up to the ion exchange depth layer, the calculation is performed by integrating up to d, which is the glass thickness, and dividing by d, so that the stress in the ion exchange depth layer has the opposite sign to the stress occurring in the non-ion exchange layer.

[0169] [Equation 14]

[0170]

[0171] In the above mathematical equation, B, V0, and γ represent the linear network dilation coefficient (LNDC), constant part of Varshneya factor, and relative concentration, respectively.

[0172] Also, if the ion exchange behaves perfectly plastically, the stress caused by the ion exchange becomes 0, and the strain distribution when it appears as a shape change is ε IC It can be defined as , and can be expressed as mathematical formula 15.

[0173] [Equation 15]

[0174]

[0175] Equations 14 and 15 illustrate two extreme cases without structural relaxation by α-relaxation. If structural relaxation by α-relaxation due to plastic deformation were to occur under these conditions, the following equations can be expressed as Equations 16 and 17.

[0176] [Equation 16]

[0177]

[0178] [Equation 17]

[0179]

[0180] Here, Ψ is a constant term for α-relaxation. The actual strain after ion exchange assumes elastic deformation, and since plastic changes such as α-relaxation occur during the stress-generating process, plastic deformation must be additionally calculated. To calculate plastic deformation, the true strain was calculated to obtain the strain value at which α-relaxation occurred, which is the simple difference between the two extreme cases, and can be expressed as the following mathematical equations 18 and 19.

[0181] [Equation 18]

[0182]

[0183] [Equation 19]

[0184]

[0185] Therefore, the change in plastic strain caused by α-relaxation in the glass after ion exchange can be expressed as in mathematical equation 20.

[0186] [Equation 20]

[0187]

[0188] The above plastic strain change refers to the change in strain that occurs plastically due to α-relaxation. By simplifying the mathematical expressions using Equations 15 to 17, the final plastic strain change can be expressed as Equation 21.

[0189] [Equation 21]

[0190]

[0191] In order to calculate the plastic curvature change in the glass that occurs with respect to the plastic strain change above, the width change was calculated. The width change that occurs at this time corresponds to the plastic strain value that varies with depth in the ion exchange depth layer, but for the purpose of simplifying the equation, the average width change up to the ion exchange depth layer was defined. Therefore, the strain expressed in mathematical equation 21 was multiplied by the width of the glass to obtain the strain, and the final width change was obtained by integrating this up to the ion exchange depth layer, which can be expressed as mathematical equation 22.

[0192] [Equation 22]

[0193]

[0194] The relative concentration γ utilized in mathematical expressions 14 to 17 and 21 to 22 can be expressed by the following mathematical expression 23.

[0195] [Equation 23]

[0196]

[0197] If we substitute Equation 23 into Equation 22, we can express it as Equation 24. Here, C s, C i and C0 represent the concentration of the exchanged alkali at the polar surface, the concentration of the corresponding alkali existing inside the glass before ion exchange, and the concentration of the alkali to be ion-exchanged existing inside the glass before ion exchange, respectively.

[0198] [Equation 24]

[0199]

[0200] It was confirmed through mathematical expression 24 that the width change that occurs plastically by α-relaxation after ion exchange can be simply expressed in terms of concentration distribution, glass width, linear network dilation coefficient (LNDC), and α-relaxation coefficient.

[0201] Figure 5 is a schematic diagram of the change in curvature caused by a change in width.

[0202] A schematic diagram of the width change that occurs when curvature occurs is illustrated in Fig. 5. The change in curvature caused by plastic width change can be calculated using simple geometric methods, and can be expressed as Equation 25 by substituting Equation 24. In this equation, for generalization, it is assumed that the width change as in Equation 24 occurs between half of the position in the ion-exchange depth layer and half of the position in the non-ion-exchange layer.

[0203] [Equation 25]

[0204]

[0205] The above mathematical expression 25 is a calculation expression for the curvature that occurs plastically due to α-relaxation. The width change is calculated using the plastic strain, and the mathematical expression for the plastic bending deformation is established using a simple geometric method through the above assumption. It was confirmed that the calculation is possible using the concentration distribution of the glass after ion exchange, the α-relaxation coefficient, and the glass thickness. The viscoelastic curvature can be expressed by simply adding the plastic curvature to the elastic curvature when mathematical expression 8 is re-expanded into an expression for curvature. Therefore, the final expression that simultaneously reflects the plastic bending deformation can be expressed as mathematical expression 26.

[0206] [Equation 26]

[0207]

[0208] Equation 26 can also be used for each curvature in Equation 9, and it simultaneously explains the plastic curvature change due to α-relaxation, which means that plastic deformation can also be intentionally induced along with stress on the glass surface.

[0209] In some embodiments, Equations 25 to 26 can be utilized to calculate additional plastic curvatures that cannot be explained by the elastic curvature based on the Stoney relation. The expression for the plastic curvature can occur under suitable conditions, such as when the ion exchange temperature is excessively high or the ion exchange time is excessively long. The suitable conditions include, for example, an ion exchange temperature of 600°C or higher and a DOL of 5 μm or higher, and preferably, an ion exchange temperature of 580°C or higher and a DOL of 10 μm or higher. However, this is for the glass used in the present invention, and it is a matter of course that when the composition of the glass is different, plastic curvatures can occur under conditions of lower or higher temperature and shorter or longer ion exchange times, and can be derived through Equations 25 to 26.

[0210] In some embodiments, the alkali type used in the exchange may be Li, not K. Since the mathematical formula provided herein can calculate the diffusion depth of the alkali moving from the outside of the glass to the inside through diffusion and the surface stress, the type of alkali penetrating into the glass may be replaced depending on whether the composition of the glass is lithium aluminosilicate (LAS) or sodium aluminosilicate (NAS), and the alkalis include Li, Na, K, Rb, Cs, etc. Depending on the type of alkali included in the parent composition of the glass and the type of alkali used in the ion exchange, the stress CS can be expressed as a negative tensile stress or a positive compressive stress, and when the stress is a negative value, the curvature can have a negative value, and when the stress is a positive value, the curvature can have a positive value. Regardless of the type of alkali, the elastic curvature can be calculated using mathematical equations 7 and 9 using the final diffusion depth, surface stress, and diffusion coefficient, and the plastic curvature can be calculated using mathematical equation 25 using glass-related constants and concentration distribution terms. Therefore, it is a matter of course that the mathematical equations provided herein are not limited to the type of alkali and the composition of glass.

[0211] In the following, unless otherwise specified in one or more examples, the plate glass used is sodium alumino-silicate glass, with a composition of 61.22SiO2- 17.02Al2O3- 11.94Na2O- 4.22K2O- 4.29MgO- 1.01ZrO2- 0.3SnO3 (wt%), a thickness of 100μm, and a size of 40×10mm. 2 am.

[0212] In one or more embodiments, the CS and DOL measured were measured via FSM, and CS or DOL obtained using optical or chemical measuring devices that measure other surface compressive stress and diffusion depth, including FSM, may also be utilized herein.

[0213] The present invention will be described in more detail through the following examples; however, the following examples are for illustrative purposes only and are not intended to limit the scope of the present invention.

[0214] [Example 1] Real-time ion exchange behavior analysis (elasticity)

[0215] In order to analyze the amount of warpage distortion caused by ion exchange, cross-sectional ion exchange was performed, and the warpage distortion caused was filmed in real time and analyzed. A slurry was prepared by adding TiO2:KNO3 in a molar ratio of approximately 34:66 to 100 ml of water solvent, and sprayed at a pressure of 8 bar from a distance of 1 m using a general gravity spray gun to form a coating film on the cross-section of the glass. The average thickness was 60 μm, and the error range by location was ± 10 μm. After drying at room temperature and 60% humidity, ion exchange heat treatment was performed at 350℃ for 90 minutes and then at 425, 440, 460, and 500℃ for 15 minutes in a furnace with a transparent quartz window. This was filmed in real time using an 8K image quality camera to measure the warpage distortion caused at 30-second intervals.

[0216] Figure 6 is a photograph of glass that has undergone deformation after ion exchange at different temperatures.

[0217] Figure 6 shows photographs of glass that exhibited warpage deformation after ion exchange heat treatment at 425°C, 440°C, 460°C, and 500°C for 15 minutes each. Although the slurry composition, coating thickness, and ion exchange time were identical, the final warpage deformation varied depending on the temperature. Furthermore, it was confirmed that large deformation occurred along one axis when using glass with a high aspect ratio.

[0218] Figure 7 is a graph showing real-time temperature measurement and glass deformation during heat treatment at 440°C for 15 minutes.

[0219] Figure 7 shows the change in the amount of warpage deformation that occurred during ion exchange at 440℃ for 15 minutes, measured at 30-second intervals for the part where the greatest phase change occurred at the exact center of the specimen, and the specimen temperature measured in real time while the ion exchange was in progress. To check the temperature inside the furnace, the tip of the temperature-measuring thermocouple was placed next to the glass to record the temperature in real time, and it was confirmed that the temperature set in the furnace and the actual recorded temperature were within the error range of ± 5℃. In addition, it was confirmed that the amount of warpage deformation gradually increased over time, but the amount of increase gradually decreased.

[0220] Figure 8 is a graph of the amount of glass deformation measured in real time according to ion exchange temperature, and Figure 9 is a graph of the rate of glass deformation measured in real time according to ion exchange temperature.

[0221] Fig. 8 shows the bending deformation measured at 30-second intervals in real time during cross-sectional ion exchange at 350℃, 425℃, 440℃, 460℃, and 500℃, and Fig. 9 shows the strain rate measured at 30-second intervals at various ion exchange temperatures. The measurements were performed at least three times for each temperature, and the average values ​​are shown. It can be confirmed that the value of the bending deformation at the same time gradually increases as the ion exchange temperature increases, but it can be confirmed that the overall deformation behavior is very similar. In addition, when checking the strain rate at 30-second intervals, it was confirmed that the deformation occurs very quickly at the beginning regardless of the temperature, and then the strain rate gradually decreases over time.

[0222] [Example 2] Application of elasticity relation (cross-sectional ion exchange)

[0223] [Example 2-1] Diffusion coefficient and effective diffusion length

[0224] The results obtained in Example 1 were used to compare the real-time bending deformation results with the calculation results using the relational formula.

[0225] Figure 10 is a graph of glass curvature measured in real time according to ion exchange temperature.

[0226] Figure 10 illustrates the results of converting the bending deformation measured in Figure 8 into curvature. By utilizing this data in the optimized Stoney relationship (Equation 8), physical properties such as CS and DOL can be determined based on the bending deformation over time, even without actual measurement using measuring equipment such as FSM. The diffusion coefficient can be utilized in this calculation.

[0227] When the composition and properties of a glass are the same, the diffusion that occurs within the glass takes the general Arrhenius form and can be expressed by mathematical equation 27 (Krynicki, Faraday Discussions of the Chemical Society 66(1978) 199).

[0228] [Equation 27]

[0229]

[0230] In mathematical expression 27, D0 is a constant, E a is the activation energy, R is the gas constant, and T is the absolute temperature. The diffusion coefficient according to the temperature can be obtained through the above mathematical equation 13, and the diffusion depth obtained through the diffusion coefficient can be obtained through the simplified mathematical equation 4 using the diffusion coefficient D as mentioned above. If the diffusion coefficient is known through mathematical equation 4, the DOL can be obtained, and the effective diffusion length can be calculated through the DOL.

[0231] Figure 11 shows the temperature-dependent diffusion coefficient of sodium alumino-silicate glass.

[0232] Figure 11 shows the temperature-dependent diffusion coefficient obtained by fitting the diffusion coefficient D obtained when the slurry composition of Example 1 is used in the sodium alumino-silicate glass used in this experiment to the mathematical expression 27.

[0233] Figure 12 shows the calculation of the effective diffusion length according to the virtual ion exchange time.

[0234] Figure 12 is a graph showing the effective diffusion length calculated for each ion exchange temperature using the data obtained in Figure 11 and plotted against an arbitrary time. The effective diffusion length was calculated using Equation 6, and was calculated with a value of α = 0.514 under the assumption that it follows the error function. Since the effective diffusion length according to the diffusion equation is simply plotted, there are differences from the curvature values ​​measured in actual experiments, but it was confirmed that overall, it shows similar behavior to the measured values.

[0235] [Example 2-2] σ0 application case

[0236] [Example 2-2-1] Application of measurement CS

[0237] Figure 13 shows the related indicators of glass used in the calculation of the relational equation, Figure 14 shows the σ0 value used in the calculation for each ion exchange temperature, Figure 15 (a) shows the change in curvature over time when CS for each ion exchange temperature is a constant σ0, and Figure 15 (b) shows the change in curvature over time for each actual ion exchange temperature.

[0238] Figure 13 illustrates the constant values ​​utilized in using Equations 7 to 8. Figure 14 illustrates the CS values ​​measured by FSM according to ion exchange conditions at each temperature. Figure 15 (a) illustrates the change in curvature over time calculated when CS for each ion exchange temperature is defined as a constant σ0 when calculating the final curvature by inputting the CS value based on Figure 12. Figure 15 (b) illustrates the change in actual curvature over time for comparison. Three data were measured for the surface where ion exchange was performed for each specimen, and the average was plotted. As a result, it was confirmed that the curvature value obtained by calculating with σ0 was very similar to the actually measured curvature value. It was confirmed that the initial deformation was almost the same as the actual measured value, but as the ion exchange time increased, it gradually deviated from that behavior and had a larger value in the calculated curvature compared to the actual measurement. It was confirmed that the deviation behavior was observed when the DOL was approximately 12 μm or more regardless of the temperature. This is confirmed by the phenomenon that the actual CS value tends to decrease over time rather than being a constant as the ion exchange time increases (Varshneya, Journal of Non-Crystalline Solids 427 (2015) 91). It can be confirmed that in actual ion exchange, the influence of the change in the σ0 value on the deformation behavior is less than that of the effective diffusion length, i.e., DOL, and therefore, σ0 can be assumed to be a constant under suitable conditions.

[0239] [Example 2-2-2] Application of CS to Curvature Variation Fitting

[0240] The experimentally obtained curvature strain reflecting the change in curvature over time was obtained, and this was fitted to the differential equation obtained by differentiating Equation 8 with respect to time, and a comparison was made with the actual measured CS value to confirm the applicability of the calculated CS. The equation obtained by differentiating Equation 8 with respect to time can be expressed as follows.

[0241] [Equation 28]

[0242]

[0243] Figure 16 shows the curvature strain over time of a cross-sectional ion-exchange glass at 425°C for 15 minutes, the behavior of the curvature strain calculated by the measured CS, and the behavior of the fitting equation.

[0244] Fig. 16 shows the curvature strain measured at 30-second intervals during cross-sectional ion exchange at 425℃ for 15 minutes, considering the change in curvature at 30-second intervals, and comparing it with the obtained deformation obtained by fitting it to Equation 28 and the curvature strain simply calculated by inputting the measured CS into Equation 28. In this case, the α value was set to 0.514. The actual measured CS is 601 ± 20 MPa, which is the value shown in Fig. 14, but the CS obtained by fitting Equation 28 to the measured curvature strain is 531 ± 36 MPa, which is a difference, but it was confirmed that the values ​​are almost similar. However, despite the existence of the difference in the values, it was confirmed that it exists within the error range of the actually measured curvature strain, and therefore, it can be confirmed that even if CS is treated as a constant that does not change over time, it does not have a large effect on the curvature.

[0245] [Example 2-2-3] CS change according to α change

[0246] Figure 17 shows the change in curvature strain fitting CS according to α at each temperature.

[0247] Fig. 17 compares the fitted CS changes according to various α values ​​for the curvature strain measured in the four temperature bands used in the experiment with the average CS by DOL measured by FSM. The difference between the fitted and measured CS in the above 2-2-2 example can usually be caused by the measurement error of stress and the difference in concentration distribution, which can be expressed as the variability of α applied to Equation 7 or Equation 28. Therefore, the change in CS obtained with various ranges of α values ​​was confirmed. As shown in Fig. 17, when the α value changes from 0 to 1, the CS can show a change of at least ~20 MPa compared to the measured value, which means that the error range by the FSM measurement can be taken into account. In addition, when the concentration distribution obtained after actual ion exchange does not follow the error function, various constants can be applied as shown in the above table. When compared to the measured average CS, it was confirmed that the values ​​were similar overall, close to α=0.514, and it was confirmed that they had the same values ​​within the error range.

[0248] [Example 2-3] Measurement CS Application Case (Reflecting Stress Relaxation Effect)

[0249] Figure 18 is about the CS measurement values ​​used for the ion exchange temperature and time-dependent calculation, and Figure 19 (a) is about the change in curvature (line) over time when CS is σ0 for each ion exchange temperature and the curvature (symbol) calculated with the measured CS, and (b) is about the change in curvature over time for each actual ion exchange temperature.

[0250] Fig. 18 shows the actual CS values ​​according to each ion exchange condition, and Fig. 19 (a) shows the symbols calculated by inserting the actual CS values ​​in Fig. 15, and Fig. 19 (b) shows the same actual curvature values. In order to correct the degree of deviation from the aforementioned CS being σ0, the curvature was calculated by inserting the actual CS values ​​for all specimens on which the actual experiment was performed, and this was expressed as a symbol. It was confirmed that when the average DOL exceeds 12 μm due to the stress relaxation effect that occurs as the actual ion exchange time increases, the symbol compared to the line assuming CS to be σ0 showed a behavior that better fits the measured curvature.

[0251] [Example 2-4] Correlation between curvature and diffusion coefficient, CS, and DOL

[0252] Figure 20 shows the expected change in curvature over time at different ion exchange temperatures, Figure 21 shows the expected change in curvature over time at different CS temperatures at 425°C, and Figure 22 shows the expected change in curvature over time at different CS temperatures at 425°C.

[0253] Fig. 20 shows the change in curvature that occurs over time according to the ion exchange temperature, i.e., the diffusion coefficient, when the properties of the glass used in the cross-sectional ion exchange are the same. Figs. 21 and 22 show the expected change in curvature according to CS that occurs over ion exchange time and DOL, respectively, at a temperature of 425℃. Referring to Fig. 20, it can be confirmed that as the temperature increases, i.e., as the diffusion coefficient increases, the curvature shows a greater deformation over time, assuming that CS has a constant value of 600.8 MPa. Fig. 21 shows that the curvature changes as CS, which has a constant value, changes under the assumption that ion exchange is performed at a temperature of 425℃, but it can be confirmed that the difference is very small compared to the diffusion coefficient. In order to confirm this once more as a change according to DOL, it is expressed in Fig. 22, and it can be confirmed that the difference in curvature deformation according to CS does not occur significantly.

[0254] [Example 2-5] Effective diffusion length suitability

[0255] Figure 23 shows the CS, DOL, and curvature measurement values ​​for each ion exchange condition used in calculating the effective diffusion length, and Figure 24 shows the effective film thickness (x-axis) calculated using the Stoney relationship and the effective diffusion length (y-axis) calculated from the concentration distribution.

[0256] Figure 23 shows the CS, DOL measured by FSM and the curvature obtained through image analysis for the glass on which the experiment was conducted under different ion exchange conditions. Figure 24 shows the effective film thickness (d) calculated by utilizing the CS measured by FSM and the curvature measured after ion exchange in the existing Stoney relation, mathematical equation 1. cal ) and the effective diffusion length (d) calculated from the concentration distribution equation used in Equation 7 eff) is compared with the values ​​calculated through mathematical formula 5. The effective film thickness can be calculated using the data in Fig. 23, and the effective diffusion length can be calculated by integrating the concentration distribution of K ions obtained by performing component analysis by line scanning on the cross-section of the glass through SEM-EDS measurement as in Fig. 2. As a result of the comparison, it was confirmed that the effective film thickness and the effective diffusion length have the same values ​​within the error range, and it was confirmed that the definition of the effective diffusion length can be applied to actual ion-exchanged glass.

[0257] [Example 2-6] Optical DOL and chemical DOL

[0258] Figure 25 shows the distribution of alkali ion concentration along the depth of a cross-section of a 7-minute cross-section ion-exchange glass at 425°C as measured by SEM-EDS, and Figure 26 shows a comparison of the optical DOL measured by FSM and the chemical DOL measured by SEM-EDS.

[0259] Fig. 25 is an example of the K concentration distribution obtained by performing SEM-EDS analysis on a cross-section of a specimen that underwent cross-sectional ion exchange heat treatment at 425°C for 7 minutes. Fig. 26 is a graph comparing the optical DOL measured by FSM and the chemical DOL (chemical DOL), which is the depth at which the K concentration converges to 0, through cross-sectional line scan for a SEM-EDS cross-sectional ion exchange specimen. In order to utilize the effective diffusion length used in mathematical equation 7, the optical DOL and the chemical DOL must be the same. Therefore, the optical DOL measured by FSM and the chemical DOL obtained through SEM-EDS cross-sectional measurement were compared. The distribution of alkali ions according to the depth measured by SEM-EDS is representatively shown in Fig. 25. The specimen was subjected to cross-sectional ion exchange heat treatment at 425°C for 7 minutes through the same slurry and coating process as Example 1. Afterwards, the coating film was lightly washed with water, dried, fractured, and a line scan was performed on the cross-section. Afterwards, the obtained K concentration according to depth was fitted with mathematical equation 3, and the depth that converges to 0 was defined to obtain the chemical DOL. The measured optical DOL and chemical DOL were then compared, and this is shown in Fig. 26. For the 14 ion exchange conditions shown in Fig. 23, the optical DOL and chemical DOL were confirmed to be the same within the error range, and thus, it was confirmed that the optical DOL can be expressed as an effective diffusion length expressed in the concept of chemical DOL.

[0260] [Example 2-7] d eff And check the suitability of 0.514*DOL

[0261] Figure 27 shows a comparison of the effective diffusion length obtained from the concentration distribution area and the effective diffusion length calculated as a constant multiple of the optically measured DOL.

[0262] In Fig. 27, the effective diffusion length calculated by SEM-EDS measurement and the effective diffusion length calculated as a constant multiple of the optical DOL measured by FSM are compared. In order to prove Equation 5, the same slurry / coating method as Example 1 was applied, and glasses for a total of 14 ion exchange temperature and time conditions were manufactured, and component analysis was performed on the K concentration in the depth direction through a cross-sectional line scan for the SEM-EDS cross-sectional ion exchange specimen, and the effective diffusion length was calculated through the integrated area. In addition, since the effective diffusion length of the concentration distribution having the form of the aforementioned error function by the mathematical method is 0.514 times the optical DOL, the effective diffusion length was calculated simply through a constant multiple of the optical DOL. The two effective diffusion lengths calculated in this way were compared, and as a result, it was confirmed that most of the values ​​were within the error range. This confirmed that the effective diffusion length can be calculated using only a constant multiple of the optical DOL measured by FSM without actual concentration analysis.

[0263] [Example 2-8] Suitability of effective stress

[0264] Figure 28 shows the CS, DOL, and curvature measurement values ​​for each ion exchange condition used in calculating the effective stress, and Figure 29 shows the effective stress (x-axis) calculated from the stress distribution obtained from the concentration distribution and the stress (y-axis) calculated using the Stoney relationship of mathematical expression 7.

[0265] Figure 28 shows the CS, effective diffusion length, and curvature obtained through image analysis for the glass subjected to experiments under different ion exchange conditions, measured by FSM. Figure 29 shows the effective stress (CS) calculated from the stress distribution assumed to be identical to the concentration distribution used in Equation 27. eff) and the stress calculated by substituting the effective diffusion length calculated from the DOL measured by FSM and the curvature measured after ion exchange into the Stoney relation, mathematical formula 7 provided by this invention, were compared. The stress can be calculated through mathematical formula 7 using the data in Fig. 28, and assuming that the stress distribution is the same as the concentration distribution of K ions obtained by performing component analysis by line scan on the cross-section of the glass through SEM-EDS measurement as in Fig. 2, the effective stress can be calculated through integration as in mathematical formula 13. As a result of the comparison, it was confirmed that the stress calculated by the Stoney relation and the effective stress have the same value within the error range, and it was confirmed that the definition of the effective stress can be applied to actual ion-exchanged glass.

[0266] [Example 2-9] CS eff Wow 0.722*CS mea Check the suitability of

[0267] Figure 30 shows a comparison of the effective stress obtained by area and the effective stress calculated as a constant multiple of the optically measured stress when the concentration distribution is assumed to be the same as the stress distribution.

[0268] In Fig. 30, the effective stress calculated by SEM-EDS measurement and the effective stress calculated as a constant multiple of the optical CS measured by FSM are compared. In order to prove Equation 13, the same slurry / coating method as Example 1 was applied and glasses were manufactured for a total of 14 ion exchange temperature and time conditions, and the component analysis was performed on the K concentration in the depth direction through a cross-sectional line scan for the SEM-EDS cross-sectional ion exchange specimen, and the effective stress was calculated through the integrated area under the assumption that the result is the same as the stress distribution. In addition, the effective stress of the stress distribution having the aforementioned error function form by a mathematical method is calculated as the optically measured CS mea As it is 0.722 times the simple CS meaThe effective stress was calculated through a constant multiple of . The two effective stresses calculated in this way were compared, and it was confirmed that most of the values ​​were within the error range. Therefore, the CS measured by FSM was used without actual concentration analysis and stress analysis. mea It was confirmed that the effective stress can be calculated using only a constant multiple of .

[0269] [Example 3] Application of the relationship (double-sided ion exchange)

[0270] [Example 3-1] Example of curvature caused by different diffusion coefficients

[0271] Figure 31 shows the heat treatment conditions and CS / DOL of the air / tin side of general float glass. Journal of the Australian Ceramic Society 57 (2021) 1331), and Fig. 32 is about the bending deformation according to the glass length, and Fig. 33 is about the diffusion coefficient of the air and tin side of general float glass ( Journal of the Australian Ceramic Society 57(2021) 1331), Fig. 34 shows the change in curvature over time obtained under heat treatment conditions of 425°C for 8 hours, and Fig. 35 shows the control of the amount of deformation under ion exchange conditions of 435°C for 12 hours of general float glass.

[0272] Figure 31 shows the CS and DOL according to the heat treatment conditions of the air and tin sides of the glass produced by the aforementioned float method, and Figure 33 shows the diffusion coefficient obtained from Figure 31 ( Journal of the Australian Ceramic Society 57 (2021) 1331). The composition of the glass is 72.33 SiO2- 13.45 Na2O- 0.06 K2O- 8.43 CaO- 4.4 MgO- 0.2 SO3 and the utilized glass is 60 × 60 mm 2The sizes are 1.1, 1.8, and 4 mm thick. The glass produced by the float method has different glass compositions on the tin side in contact with the tin bath and the air side exposed to the air due to the tin, which directly leads to a difference in diffusion coefficient. If you check the CS / DOL of the air and tin sides according to the heat treatment conditions in Fig. 31, you can see that the DOL is consistently lower on the tin side. Using the DOL data obtained in Fig. 31, you can obtain the diffusion coefficient as in Fig. 33, and you can see that the diffusion coefficient of the tin side shows a lower value than the diffusion coefficient of the air side. When using the diffusion coefficient and an arbitrary CS, you can predict the warpage deformation caused by the inherent difference in the diffusion coefficient of the float glass. For example, when ion exchange is performed at 425℃ for 8 hours and the obtained CS is used as σ0, the deformation that appears over time can be calculated by calculating the curvature as in Fig. 34. However, it can be confirmed that the amount of deformation is significantly smaller because the thickness of the glass is formed thicker than in other examples. Figure 34 shows the specimen size of 60 × 60 mm. 2 This is the result calculated. In the case of actual float glass, since the size of the original glass differs by up to about 6 m, the warpage deformation due to the difference in the innate diffusion coefficient becomes a major problem, and this is illustrated in Figure 32. It can be confirmed that the amount of warpage gradually increases as the length of the glass increases, and as a result, the float glass has a warpage that cannot be ignored when the existing immersion ion exchange is performed due to the difference in the diffusion coefficient.

[0273] [Example 3-2] Example of non-occurrence of curvature due to different diffusion coefficients

[0274] Figure 36 shows the conditions for non-deformation and the difference in curvature radius of the air / tin side in general float glass.

[0275] In this regard, 1 / R in Fig. 36before and 1 / R after The unit of cm is R before and R after , which means the unit of 1 / R before and 1 / R after The actual unit is 1 / cm.

[0276] Fig. 36 shows the expected CS and DOL without deformation by adjusting σ0 or DOL of the air side when σ0 and DOL of the tin side are maintained using the diffusion coefficient and σ0 obtained in Fig. 23. Fig. 35 shows the change in curvature over time for one of the data of Fig. 36. Through the above-described examples, it can be seen that the CS or DOL formed on the glass surface can be controlled by adjusting the composition, thickness, etc. of the slurry, and thus the CS or DOL as in Fig. 36 can be formed. Therefore, when the curvature is 0, the bending deformation according to the glass length is also fixed to 0, so that a specific condition in which deformation does not occur regardless of the glass length can be established. Fig. 35 shows the change in curvature over time when the bending deformation becomes 0 under ion exchange conditions at 435°C for 12 hours. It can be confirmed that the bending deformation continuously converges to 0 regardless of time.

[0277] [Example 4] Example of stress by calculation

[0278] Figure 37 relates to the relevant parameters of soda-lime silicate glass used in stress calculations (Macrelli, International Journal of Applied Glass Science 11 (2020) 730).

[0279] Figure 37 is a table showing parameters for calculating stress distribution and CS obtained from the concentration distribution of ion-exchanged alkali ions using mathematical equation 12. The composition of the glass from which the parameters were derived is 70.98 SiO2- 0.57 Al2O3- 0.03 Fe2O -3 - 0.04 TiO2- 12.85 Na2O - 0.04 K2O - 8.87 CaO - 6.44 MgO - 0.15 SO3(mol%) (Macrelli, International Journal of Applied Glass Science 11 (2020) 730). In this calculation, the thickness-wise concentration distribution of the ion-exchanged alkali ions was assumed to follow a typical error function model as in Equation 3, and the surface relative concentration of the ion-exchanged alkali ions was assumed to be 0.9.

[0280] Figure 38 shows the calculated value of CS according to changes in thickness and DOL, and Figure 39 shows the change in CS according to changes in DOL and thickness.

[0281] Figure 38 shows the CS calculation results when DOL is 10, 30, 50 and 100 μm in soda-lime silicate glass having a thickness of 1.0, 2.0 and 3.0 mm, respectively, and Figure 39 is a drawing showing the CS results of Figure 38 with respect to DOL. According to the CS calculation results described in Figures 38 and 39, it was confirmed that the calculated CS decreases as the thickness of the glass and DOL increase. When the ratio of DOL to the thickness of the glass increases, the total average concentration of ion exchange, C, in Equations 10 and 12 *As (t) increases, CS shows a decreasing behavior. The change in CS value calculated from the data in Figs. 38 and 39 was confirmed to have a difference of up to ± 15 MPa in the thickness range of 1.0-3.0 mm and DOL range of 10-100 μm, and it can be confirmed that the difference is within about 4% compared to the average CS.

[0282] [Example 4] Real-time ion exchange behavior analysis (carbonaceous)

[0283] In order to analyze the amount of warpage deformation induced by ion exchange, cross-sectional ion exchange was performed, and the warpage deformation was filmed in real time and analyzed. A coating film was formed on the cross-section of the glass under the same conditions as Example 1, and the average thickness was 60 μm, and the error range by location was ± 10 μm. After drying at room temperature and 60% humidity, ion exchange heat treatment was performed at 580°C for 1 minute 30 seconds and 600°C for 2 minutes in a furnace equipped with a transparent quartz window, and this was filmed in real time using a camera with an 8K image quality, and the warpage deformation that occurred was measured at 30-second intervals.

[0284] Figure 40 is a graph of the amount of glass deformation measured in real time according to ion exchange temperature, and Figure 41 is a graph of the rate of glass deformation measured in real time according to ion exchange temperature.

[0285] Fig. 40 shows the bending deformation measured at 30-second intervals in real time during cross-sectional ion exchange at 580℃ and 600℃, and Fig. 41 shows the strain rate measured at 30-second intervals at various ion exchange temperatures. The measurements were performed at least three times for each temperature, and the average values ​​are shown. It can be confirmed that the value of the bending deformation at the same time gradually increases as the ion exchange temperature increases, but it can be confirmed that the overall strain behavior is very similar. In addition, when checking the strain rate at 30-second intervals, it was confirmed that the deformation occurs very quickly at the beginning regardless of the temperature, and then the strain rate gradually decreases over time.

[0286] [Example 5] Application of the relational equation (cross-sectional ion exchange, carbon-carbon)

[0287] [Example 5-1] Measurement of plastic curvature

[0288] Figure 42 relates to the relevant indices of glass used in the calculation of the relational equation, and Figure 43 relates to the CS, DOL, and curvature measurement values ​​used in the calculation according to the conditions for each ion exchange temperature.

[0289] The results obtained in Example 4 were used to compare the real-time bending deformation results with the calculation results using the relational formula.

[0290] Figure 44 is a graph of glass curvature measured in real time according to ion exchange temperature.

[0291] Figure 44 shows the result of converting the bending deformation measured in Figure 40 into curvature. By utilizing the data in the optimized Stoney relation in Equation 8, the material properties such as CS and DOL can be determined by the bending deformation over time without the need for actual measurement using measuring equipment such as FSM. The diffusion coefficient can be utilized in the calculation. In addition, since the ion exchange temperature may additionally cause plastic deformation, the measured width change can be utilized through the optimized plastic deformation relation in Equation 25 to determine the concentration distribution, α-relaxation-related coefficients, etc.

[0292] Figure 45 is a graph of the glass plasticity curvature measured in real time according to ion exchange temperature.

[0293] In Fig. 45, the elastic curvature was calculated using Equation 8 and Figs. 42 to 43, and the plastic curvature measured through the difference of the elastic curvature calculated from the measured curvature value using Equation 26 was shown. For an accurate comparison, the results including the conditions of Example 1 as well as Example 4 were shown. It was confirmed that the excessively high ion exchange temperature caused a plastic shape change, and as a result, the difference in curvature occurred at a level that exceeded the error range only at 580°C and 600°C. In particular, it was confirmed that the plastic curvature occurred gradually over time at 580°C, and that the plastic curvature occurred from the beginning of the ion exchange at 600°C.

[0294] [Example 5-2] Width change application example

[0295] Figure 46 is a graph comparing the calculated plastic curvature and the actual curvature according to ion exchange conditions.

[0296] In Fig. 46, the measured plastic curvature values ​​over time at 580℃ and 600℃ among the data shown in Fig. 45 are compared with the calculated plastic curvature values ​​calculated using the above mathematical expression 25. The plastic curvature values ​​were calculated using the concentration distribution measured by Fig. 42 and SEM-EDS, and when compared with the data shown in Fig. 45, it was confirmed that they showed very good matching behavior. As a result, it was confirmed that the plastic bending strain obtained through mathematical expression 25 can define a plastic strain that deviates from the Stoney relation that describes the elastic bending strain. Through this, it can be confirmed that the final bending strain can be accurately calculated even under conditions where plastic deformation occurs by using mathematical expression 26. Here, although the same parameter values ​​as in Fig. 42 were used in the glass composition and size used in this example, it is a matter of course that the values ​​of the corresponding parameters may be different if the glass composition or size is different.

[0297] [Example 6] Real-time ion exchange behavior analysis (using LiNO3)

[0298] To analyze the warpage deformation caused by ion exchange, the warpage deformation caused by cross-sectional ion exchange was filmed in real time and analyzed. A slurry was prepared by adding TiO2:LiNO3 in a molar ratio of approximately 63:37 to 100 ml of water solvent, and sprayed at a pressure of 8 bar from a distance of 1 m using a general gravity spray gun to form a coating film on the cross-section of the glass. The average thickness was 60 μm, and the error range by location was ± 10 μm. After drying at room temperature and 60% humidity, ion exchange heat treatment was performed in a furnace with a transparent quartz window for 15 minutes at 200℃, 12 minutes at 250℃, 5.3 minutes at 280℃, 3.2 minutes at 300℃, 2 minutes at 320℃, and 0.8 minutes at 350℃. This was filmed in real time using an 8K image quality camera to measure the amount of bending deformation that occurred at 30-second intervals.

[0299] Figure 47 is a photograph of a glass that was deformed after ion exchange at different temperatures using LiNO3 slurry.

[0300] Figure 47 is a photograph of glass that underwent warpage after undergoing ion exchange heat treatment at 200°C for 15 minutes. Similar to Example 1, a coating film was formed on the upper side of the glass, but the warpage deformation occurred with a negative value, and it was confirmed that warpage occurred along one axis by using glass with a large aspect ratio.

[0301] Figure 48 is a graph of the curvature of glass measured in real time according to ion exchange temperature.

[0302] Fig. 48 shows the curvature calculated from the bending deformation measured in real time at 30-second intervals during cross-sectional ion exchange at 200, 250, 280, 300, 320, and 350°C. The measurements were performed at least three times for each temperature, and the average values ​​are shown. It can be seen that tensile stress rather than compressive stress is generated on the surface as the alkali with a smaller ionic radius than the alkali inside the glass diffuses into the glass, which causes negative stress and thus obtains a negative curvature value. In addition, it can be confirmed that the absolute value of the curvature gradually increases at the same time as the ion exchange temperature increases, but the overall deformation behavior is similar and can be confirmed to show a behavior similar to that of Example 1.

[0303] The above description of the present invention is for illustrative purposes only, and those skilled in the art will readily appreciate that the present invention can be readily modified into other specific forms without altering the technical spirit or essential characteristics of the present invention. Therefore, the embodiments described above should be understood as illustrative in all respects and not restrictive. For example, each component described as a single entity may be implemented in a distributed manner, and similarly, components described as distributed may be implemented in a combined manner.

[0304] The scope of the present invention is indicated by the claims described below rather than the detailed description above, and all changes or modifications derived from the meaning and scope of the claims and their equivalent concepts should be interpreted as being included in the scope of the present invention.

Claims

1. A method for determining the amount of bending deformation of plate glass, In the temperature range where elastic deformation occurs, the radius of curvature of the plate glass corresponding to the amount of bending deformation of the plate glass is determined based on the Stoney relation, A method for determining the amount of warpage deformation of plate glass, wherein the first and second layers included in the above Stoney relationship are set to be the first layer by the thickness corresponding to the effective diffusion length among the thickness of the plate glass, and the second layer by the thickness excluding the effective diffusion length among the thickness of the plate glass, based on the integrated value of the concentration distribution up to the ion exchange depth layer after ion exchange of the glass including alkali and the effective diffusion length, which is the depth calculated to have the same area under the assumption that the same surface concentration is the same according to the depth.

2. In paragraph 1, A method for determining the bending deformation of plate glass, wherein the diffusion coefficient in the above Stoney relationship is a value calculated by inversely calculating the depth of layer obtained after the ion exchange.

3. In paragraph 1, The above effective diffusion length is a method for determining the bending deformation of plate glass, which is a value calculated through parameters set in consideration of the error range that occurs for the measurement of compressive stress and the stress that causes bending deformation and the diffusion depth obtained after the ion exchange.

4. In paragraph 1, The method for determining the bending deformation of the above plate glass is as follows: In the temperature range where plastic deformation occurs, the radius of curvature of the plate glass is determined by a simple sum of viscoelastic curvatures, reflecting the plastic curvature of the plate glass corresponding to the amount of bending deformation of the plate glass based on the elastic-plastic strain-based relationship together with the Stoney relationship. A method for determining bending strain of plate glass, wherein the plastic strain included in the above-mentioned elastic strain-based relationship is based on the width change that appears in the plate glass after ion exchange through the shape change that occurs due to the structural relaxation effect caused by α-relaxation.

5. In paragraph 4, The above plastic curvature is, A method for determining the bending deformation of plate glass, wherein the average width change occurring up to the ion exchange depth layer is calculated as a plastic curvature that occurs under the assumption that the width change is constant up to the ion exchange depth layer.

6. In paragraph 4, The above elastic strain is, A method for determining the amount of bending deformation of plate glass, which is a value calculated through a relationship based on the structural relaxation effect caused by α-relaxation that occurs differently depending on the ion exchange temperature and time during ion exchange.

7. In paragraph 4, The above width change is, A method for determining the amount of bending deformation of plate glass, wherein the bending deformation is calculated from the plastic strain among the above-mentioned elastic strains and the width value of the plate glass, and the value changes depending on the concentration from the glass surface to just before the ion exchange layer, and the value is calculated by averaging the width change up to the ion exchange depth layer through integration.

8. In paragraph 7, The above plastic curvature is, A method for determining the bending deformation of plate glass, wherein the value is calculated by assuming that the width change occurs in a thickness change from half the depth of the ion exchange layer to half the depth of the ion exchange depth layer through a simple geometric method utilizing the above width change.

9. In paragraph 4, The above viscoelastic curvature is, A method for determining the bending deformation of plate glass, wherein the value is calculated as a simple sum of the elastic curvature, which is the bending deformation amount based on the above Stoney relation, and the plastic curvature, which is the bending deformation amount based on the above elastic-plastic strain-based relation.

10. A method for manufacturing glass using the method for determining the amount of bending deformation of plate glass according to Article 1, A method for manufacturing glass that causes a bending deformation corresponding to the radius of curvature in the plate glass through ion exchange of glass containing the alkali corresponding to the radius of curvature determined by the method for determining the amount of bending deformation of the plate glass.

11. Glass manufactured by the method according to Article 10, In the temperature range where elastic deformation occurs, Glass manufactured so that bending deformation occurs corresponding to a preset relationship between the curvature, compressive stress, and effective diffusion length of the glass derived based on the Stoney relationship that reflects the above assumptions and the settings for the first and second layers.

12. In paragraph 11, In the temperature range where plastic deformation occurs, Glass manufactured to correspond to a predetermined relationship between the curvature, compressive stress, effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width change that appears after ion exchange in the plate glass, which is derived based on the elastic-plastic strain-based relationship along with the above Stoney relationship.

13. Glass manufactured by the method according to Article 10, In the temperature range where elastic deformation occurs, In response to the ion exchange occurring on the first side of the two sides of the above-mentioned plate glass, a preset relationship between the curvature, compressive stress, and effective diffusion length of the glass derived based on the Stoney relationship that reflects the above-mentioned assumptions and the settings for the first layer and the second layer, and In response to the ion exchange occurring on the second side of the two sides of the above-mentioned plate glass, a preset relationship between the curvature, compressive stress, and effective diffusion length of the above-mentioned glass, derived based on the Stoney relationship that reflects the above-mentioned assumptions and the settings for the first layer and the second layer, Glass manufactured so that bending deformation corresponding to the 14. In paragraph 13, In the temperature range where plastic deformation occurs, In response to ion exchange occurring on the first side of both sides of the above-mentioned plate glass, a pre-set relationship between curvature, compressive stress, and effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width of the above-mentioned glass is derived based on an elastic-plastic strain-based relationship that reflects a setting for a width change that appears after ion exchange in the above-mentioned plate glass, together with a Stoney relationship that reflects the above-mentioned assumption and the settings for the first layer and the second layer, and Glass manufactured so that bending deformation occurs corresponding to a preset relationship between curvature, compressive stress, and effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width of the glass, which is derived based on an elastic-plastic strain-based relationship that reflects the setting for the width change, together with a Stoney relationship that reflects the setting for the first layer and the second layer, in response to ion exchange occurring on the second side among the two sides of the above-mentioned plate glass.

15. Glass manufactured by the method according to Article 10, In the temperature range where elastic deformation occurs, In response to ion exchange occurring in the first region among the regions on both sides of the above-mentioned plate glass, a preset relationship between the curvature, compressive stress, and effective diffusion length of the glass derived based on the Stoney relationship that reflects the above-mentioned assumption and the settings for the first layer and the second layer, and In response to ion exchange occurring in a second region different from the first region among the regions on both sides of the above-mentioned plate glass, a predetermined relationship between the curvature, compressive stress, and effective diffusion length of the glass derived based on the Stoney relationship that reflects the assumption and the settings for the first layer and the second layer, Glass manufactured so that bending deformation corresponding to the 16. In paragraph 15, In the temperature range where plastic deformation occurs, In response to ion exchange occurring in a first region among the regions on both sides of the above-mentioned plate glass, a pre-set relationship between curvature, compressive stress, and effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width of the above-mentioned glass derived based on an elastic-plastic strain-based relationship that reflects a setting for a width change that appears after ion exchange in the above-mentioned plate glass, together with a Stoney relationship that reflects the above-mentioned assumption and the settings for the first layer and the second layer, and Glass manufactured so that bending deformation occurs corresponding to a preset relationship between curvature, compressive stress, and effective diffusion length, alkali concentration distribution, α-relaxation coefficient, and width of the glass, which is derived based on an elastic-plastic strain-based relationship that reflects the setting for the width change, together with a Stoney relationship that reflects the setting for the first layer and the second layer, in response to ion exchange occurring in a second region different from the first region among the regions on both sides of the glass.

Images