KR102390428B1 - Fabrication of Thermoelectric Materials with Enhanced Seebeck Coefficient through Localized Surface Plasmonic Resonance Gating - Google Patents

Abstract

An object of the present invention is to provide a thermoelectric material having an increased Seebeck coefficient and a method for manufacturing the same. The thermoelectric material according to the present invention includes a thin or thick film made of ZnO or a ZnO substrate made of a bulk material; and Ag nanoparticles formed on the ZnO substrate, wherein the Ag nanoparticles absorb light to cause absorption amplification by plasmonic resonance to increase the Seebeck coefficient of the ZnO.

Description

Fabrication of Thermoelectric Materials with Enhanced Seebeck Coefficient through Localized Surface Plasmonic Resonance Gating

The present invention relates to a thermoelectric material and a method for manufacturing the same, and more particularly, to a ZnO-based thermoelectric material and a method for manufacturing the same.

While interest in the development and saving of alternative energy is on the rise, research on efficient energy conversion materials is being actively conducted. In particular, research on thermoelectric materials, which are thermal-electrical energy conversion materials, is accelerating.

If there is a temperature difference at both ends of the material in the solid state, the concentration difference of carriers (electrons or holes) with thermal dependence also occurs at both ends, and this appears as an electrical phenomenon called thermoelectricity, that is, a thermoelectric phenomenon. As such, the thermoelectric phenomenon refers to a reversible and direct energy conversion between a temperature difference and an electric voltage. This thermoelectric phenomenon can be divided into thermoelectric power generation that produces electrical energy, and thermoelectric cooling/heating that causes a temperature difference between both ends by supplying electricity, and the material exhibiting such a thermoelectric phenomenon is a thermoelectric material.

Thermoelectric materials are eco-friendly and sustainable because they do not emit pollutants during power generation and cooling, so many studies are being conducted. In particular, there is a high interest in renewable energy-related fields that can generate electricity directly from waste heat generated from incinerators or various industrial facilities, or from natural heat such as solar heat, geothermal heat, and river water heat for energy harvesting.

As a factor for measuring the performance of the thermoelectric material, a dimensionless figure of merit ZT defined as in Equation 1 below is used.

<Equation 1>

(Where S is the Seebeck coefficient, σ is electrical conductivity, T is absolute temperature, and κ is thermal conductivity.)

In order to increase ZT, the Seebeck coefficient and electrical conductivity, that is, the power factor (S ² σ), should be increased and the thermal conductivity should be decreased. Most of the studies have been trying to increase the Seebeck coefficient as a strategy to increase the ZT. In the meantime, there have been many studies on charge concentration control through doping a specific impurity or changing the crystal structure or composition of a material to increase the Seebeck coefficient, but further improvement is needed.

1 is a graph showing a correlation between variables determining ZT according to an impurity doping concentration. As shown in Fig. 1, since the Seebeck coefficient has a trade-off relationship with electrical conductivity and thermal conductivity, which are other elements of ZT, the factor introduced to increase the Seebeck coefficient is the electrical conductivity and thermal conductivity. It is not easy to independently increase only the Seebeck coefficient without degrading the thermoelectric performance of the material by changing it.

The present invention was devised to solve the above problems, and an object of the present invention is to provide a thermoelectric material having an increased Seebeck coefficient and a method for manufacturing the same.

Other objects and advantages of the present invention may be understood by the following description, and will become more clearly understood by the examples of the present invention. It will also be readily apparent that the objects and advantages of the present invention may be realized by means of the instrumentalities and combinations thereof indicated in the claims.

In order to achieve the above object, the thermoelectric material according to the present invention includes a thin or thick film made of ZnO or a ZnO substrate made of a bulk material; and Ag nanoparticles formed on the ZnO substrate, wherein the Ag nanoparticles absorb light to cause absorption amplification by plasmonic resonance to increase the Seebeck coefficient of the ZnO.

In the present invention, in the thermoelectric material, the concentration of free electrons increases by excitation of electrons in response to light having a wavelength exceeding 425 nm.

In the present invention, the thermoelectric material is used with a means for operating in sunlight or illuminating the light.

A method for manufacturing a thermoelectric material according to the present invention comprises the steps of: preparing a ZnO substrate made of a thin or thick film or bulk material made of ZnO; and forming Ag nanoparticles on the ZnO substrate.

In the present invention, the manufacturing of the ZnO substrate comprises: preparing a Zn source solution; forming a ZnO thin film by applying the Zn source solution; and heat-treating the ZnO thin film.

In the present invention, the Zn source solution may be prepared by stirring zinc acetate (Zinc-acetate) in a solution of methoxyethanol (2-Methoxyethalnol) mixed with ethanolamine (Ethanolamine).

In the present invention, the forming of the Ag nanoparticles may include depositing Ag in a thermal evaporator to form Ag nanoparticles.

According to the present invention, silver (Ag) nanoparticles are deposited on the surface of zinc oxide (ZnO) to induce absorption amplification through surface plasmonic resonance and optical gating thereby to control the concentration and mobility of charges. Thus, it is possible to increase the Seebeck coefficient while increasing the electrical conductivity of the material, and by using ZnO with the increased Seebeck coefficient, it can be widely applied to thermoelectric devices, optical sensors, and photo-thermo voltaic fields.

The present invention can more effectively tune the Seebeck coefficient of ZnO by controlling the charge concentration and the scattering center concentration according to the size, shape, or deposition thickness of Ag nanoparticles.

According to the present invention, it is possible to increase the thermoelectric efficiency by increasing the Seebeck coefficient of ZnO. The manufacturing method for improving and optimizing the Seebeck coefficient of a thermoelectric material through surface plasmonic gating according to the present invention can be utilized in various fields of using thermoelectric materials.

The following drawings attached to this specification illustrate preferred embodiments of the present invention, and serve to further understand the technical spirit of the present invention together with the detailed description of the present invention to be described later, so that the present invention is a matter described in those drawings should not be construed as being limited only to
1 is a graph showing a correlation between variables determining ZT according to an impurity doping concentration.
2 is a flowchart schematically illustrating a method for manufacturing a thermoelectric material according to the present invention.
3 is a schematic diagram of a thermoelectric material according to the present invention.
4 is a view for explaining the plasmonic effect and Ag nanoparticles deposited on ZnO.
5 is a schematic diagram of a copper block stage used in the experiment.
6 is a graph showing the absorbance of ZnO and the absorbance of Ag nanoparticles by increased Ag nanoparticles.
7 is an SEM image of Ag nanoparticles deposited on ZnO.
8 is a graph showing a change in the Seebeck coefficient according to time when light is irradiated in the experimental examples.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. Prior to this, the terms or words used in the present specification and claims should not be construed as being limited to conventional or dictionary meanings, and the inventor should properly understand the concept of the term in order to best describe his invention. Based on the principle that it can be defined, it should be interpreted as meaning and concept consistent with the technical idea of the present invention.

Accordingly, the configuration shown in the embodiments and drawings described in the present specification is only the most preferred embodiment of the present invention and does not represent all of the technical spirit of the present invention, so at the time of the present application, various It should be understood that there may be equivalents and variations.

Recently, the study of optical and electrical properties of ZnO is being actively conducted. ZnO is a ceramic material and a semiconductor material with a wide direct bandgap. Although it is transparent, conductivity exists. Above all, it is a material widely used in devices such as varistors, solar cell transparent electrodes, sensors, and lasers because of the advantage that it can be applied to a wide range of defect chemistry. Most of the active studies are focused on understanding the electrical and optical properties according to the ZnO thin film formation method. However, ZnO is a material in which thermoelectric properties are clearly observed, and a thermoelectric voltage can be observed when a temperature difference is made. The present inventors paid attention to the thermoelectric properties of ZnO, developed a platform that can confirm the behavior of charge carriers in a ZnO thin film, and studied a method for increasing the Seebeck coefficient of a thermoelectric material containing ZnO, leading to the present invention.

As mentioned above, most of the techniques for increasing the Seebeck coefficient in the conventional thermoelectric material field are control of the charge concentration through doping of a specific impurity, a phase change of a material's crystal structure, and a composition change. In particular, in the case of ZnO, many studies have been conducted through doping with Li and Mg, and recently, there has been a report on the photo seebeck effect through light. However, in this approach, tuning the Seebeck coefficient has been considered to be very complicated because the change in the Seebeck coefficient is closely related not only to the charge concentration but also to the charge scattering center. The present invention solves this multi-step by optical gating through a simple process of forming Ag nanoparticles, and it is not only simple, but also the charge concentration and the scattering center concentration according to the size, shape, or deposition thickness of the Ag nanoparticles. It has the advantage of being able to more effectively tune the Seebeck coefficient by controlling it.

2 is a flowchart schematically illustrating a method for manufacturing a thermoelectric material according to the present invention.

First, a thin film or thick film made of ZnO, which is the basis of the thermoelectric material, or a ZnO substrate made of a bulk material is prepared (step S10). The ZnO substrate may be formed by a thin film formation method such as a sintering method, a solution coating method, a vapor deposition method, or a sputtering method.

Next, Ag nanoparticles are formed on the ZnO substrate (step S20). A method of forming Ag nanoparticles may be a vapor deposition method or a coating method using a solution of Ag nanoparticles. Ag nanoparticles may completely or partially cover the surface of the ZnO substrate. The Seebeck coefficient of the ZnO substrate can be more effectively tuned by controlling the charge concentration and the scattering center concentration according to the size, shape, or deposition thickness of Ag nanoparticles.

By such a simple two-step method, the thermoelectric material according to the present invention has a structure as shown in FIG. 3 . The thermoelectric material 100 according to the present invention has a structure in which a ZnO substrate 110 and Ag nanoparticles 120 are complexed, and in particular, has a structure in which Ag nanoparticles 120 are formed on the surface of the ZnO substrate 110 . . According to the present invention, it is possible to increase the thermoelectric efficiency by increasing the Seebeck coefficient of ZnO, which is the basis of the thermoelectric material 100 .

FIG. 4 is a view for explaining the plasmonic effect and Ag nanoparticles 120 deposited on the thin-film ZnO substrate 110 formed on the glass substrate 105 .

Surface Plasmon Resonance (SPR) is when a sufficiently small (nano-scale) conductor (metal) with a large number of free electrons is in contact with a dielectric whose dielectric constant is different from that of the conductor, the electrons present on the surface It is a phenomenon in which the free electrons on the surface of the conductor collectively vibrate by resonating with the electromagnetic field of light of a specific wavelength, thereby forming a local strong electric field. It amplifies the electric field of light of a specific wavelength through plasmonic resonance. Finally, through the local electric field generated on the surface, it shows the effect of strengthening the intensity of light of a specific wavelength that hits the dielectric surface. Depending on the type, size, shape, and arrangement of the conductor formed on the dielectric, the wavelength band of the reaction light can be adjusted.

In the present invention, Ag nanoparticles 120 are used as a sufficiently small (nano-scale) conductor (metal). In addition, the ZnO substrate 110 is used as a dielectric different from the dielectric constant of the conductor. As shown in FIG. 4 , when the Ag nanoparticles 120 are in contact with the ZnO substrate 110 , electrons present on the surface resonate with the electromagnetic field of the light of a specific wavelength (Light in FIG. 4 ), so that the Ag nanoparticles The free electrons on the surface of the particles 120 collectively vibrate, thereby forming a locally strong electric field. Through the plasmonic resonance phenomenon, the Ag nanoparticles 120 amplify the electric field of light having a wavelength in the visible light region corresponding to the plasmonic resonance frequency. As a result, the ZnO substrate 110 has an effect of strengthening the intensity of the light having a wavelength in the visible region that hits the surface.

The absorption region of ZnO, which absorbs the UV wavelength region, is expanded to the visible region by the attached Ag nanoparticles 120, and through this, more electrons can be excited. As shown in FIG. 4, charge transfer through the formation of a hot-electron with high energy that can be transferred from the Ag nanoparticles 120 to the ZnO substrate 110 through plasmonic decay is in the ZnO proposed in the present invention. The charge concentration in the optical gating is a key concept. Tuning of charge concentration increase by charge transfer through UV absorption and hot-electron formation in ZnO and charge concentration decrease by charge trap in the scattering center present between ZnO and Ag nanoparticles shown in FIG. We want to realize the maximized Seebeck coefficient through Structural defects due to discontinuity of bonding at the ZnO/Ag interface serve to trap and reduce the charge concentration.

In this way, the concentration and mobility of the charge of the thermoelectric material 100 including the ZnO substrate 110 can be controlled by causing absorption amplification through the surface plasmonic resonance phenomenon, and thereby inducing optical gating and charge trap sites. . Accordingly, it is possible to increase the Seebeck coefficient while controlling the electrical conductivity of the entire thermoelectric material 100, and by using the thermoelectric material 100 with the increased Seebeck coefficient, it can be widely applied to thermoelectric devices, optical sensors, and photo-thermal mechanisms. there is.

The present invention is not an efficiency improvement method that incurs costs such as chemical doping of a material or device integration, but a method of increasing the efficiency of the Seebeck effect using the intrinsic properties of the material. When ZnO receives light of a specific wavelength, electrons are excited and the effect of increasing the concentration of free electrons can be expected. Using this effect, optical electron injection can be applied. Thus, it is possible to achieve an increase in thermoelectric efficiency through the improvement of the generated charge transfer characteristics. In addition, when Ag nanoparticles 120 are formed on the surface of the ZnO substrate 110 to amplify this effect, the effect of optical electron injection can be increased through the surface plasmonic effect.

The thermoelectric material may have a significant difference in thermoelectric performance depending on the manufacturing method. The thermoelectric material according to the present invention is manufactured by the above-described method for manufacturing the thermoelectric material, and a large ZT can be secured by increasing the Seebeck coefficient.

The thermoelectric material according to the present invention has a large Seebeck coefficient and electrical conductivity, and has excellent thermoelectric conversion performance due to low thermal conductivity. Therefore, the thermoelectric material according to the present invention can be effectively used in a thermoelectric device in addition to or replacing the conventional thermoelectric material. The thermoelectric element, thermoelectric module, and thermoelectric device including the thermoelectric material may be, for example, a thermoelectric cooling system or a thermoelectric power generation system, and the thermoelectric cooling system may include a general-purpose cooling device such as a refrigerant-free refrigerator and air conditioner, a micro cooling system, An air conditioner, a waste heat power generation system, and the like may be mentioned, but the present invention is not limited thereto. The configuration and manufacturing method of the thermoelectric cooling system are known in the art, and detailed description thereof will be omitted herein.

Hereinafter, the effects of the present invention will be described in detail through the experimental examples of the present invention. Below, examples and comparative examples will be described in detail to explain the present invention in more detail. However, the embodiment according to the present invention may be modified in various other forms, and the scope of the present invention should not be construed as being limited to the embodiment described in detail below. The embodiments of the present invention are provided to more completely explain the present invention to those of ordinary skill in the art.

(Experimental example)

The increase in thermoelectric efficiency was confirmed by a simple method of irradiating light without any material change. In addition, it was confirmed that such an effect was amplified when Ag nanoparticles were deposited as presented in the present invention, and it was confirmed that the Seebeck effect efficiency increased at a wider wavelength. A thermoelectric material sample according to an embodiment of the present invention was prepared in the following manner.

1) Zn source solution preparation

In a solution of methoxyethanol (2-Methoxyethalnol) as a solvent and 1.6 M of ethanolamine as a stabilizer, 1.6 M of zinc-acetate as a Zn precursor was stirred at 75 ° C. for 2 hours on a stirrer. A Zn source solution was prepared. The prepared Zn source solution was prepared by aging at room temperature for 48 hours.

2) Filter the Zn source solution prepared in 1) using a PTFE (polytetrafluoroethylene) syringe filter with a pore size of 0.2 um, and then filter the Zn source solution on the cleaned glass substrate for 3 seconds at 600 RPM, A two-step spin coating process was performed at 2500 RPM for 60 seconds. The thin film formed by this method of applying the solution was dried on a 100°C heater for 10 minutes, and then baked on a 250°C heater to form a high-density, 100nm-thick ZnO thin film.

3) RTA (Rapid Thermal Annealing) process

In order to improve the crystallinity and electrical properties of the ZnO thin film formed in 2), the RTA process was performed in an oxygen atmosphere at 500 °C for 1 hour. The RTA control system is a PID output control, which controls the output of the halogen lamp to increase the temperature quickly (PID is a function value for each output control). The temperature increase was instantaneously performed at a temperature of about 10° C. per second. The RTA process can be omitted as one of the process steps for improving the performance of ZnO.

4) Ag nanoparticles deposition

The RTA ZnO thin film prepared above was loaded on a thermal evaporator, and 3 nm of Ag was deposited at a rate of 2 Å/sec to deposit Ag nanoparticles on the ZnO thin film.

For comparison, a comparative example sample consisting only of a ZnO thin film in which Ag nanoparticles were not deposited was also prepared.

5 is a schematic diagram of a copper block stage used in the experiment. The Seebeck coefficient was measured using the copper block stage 200 .

The copper block stage 200 includes a pair of copper blocks 210 and 220 , a multimeter 230 , and a clamp 240 . A sample 250 to be measured is placed on the copper blocks 210 and 220 . The sample 250 is prepared above, and includes a ZnO thin film 110 ′ on a glass substrate 105 ′. In particular, the sample according to the invention further comprises Ag nanoparticles. A pair of Al electrodes 140 spaced apart at intervals of 1 mm were formed on the top of the sample 250 .

Clamps 240 are attached to the front portions of both ends of the copper blocks 210 and 220 . Physical contact between the copper blocks 210 and 220 and the sample 250 may be improved by using the clamp 240 .

The temperature of one end of the copper block 210 is raised using a cartridge heater (not shown), thereby generating a temperature gradient between both ends of the copper blocks 210 and 220 . 5, the heated copper block 210 is 'HOT', and the copper block 220 that is not heated is 'COLD'. The copper blocks 210 and 220 have excellent thermal conductivity. Therefore, one end of the copper block 210 allows the heating of the heater to be transmitted to the sample 250 well and to form a high temperature end of the sample 250 . The copper block 220 at the other end is a heat dissipator, so that the heat transferred from the sample 250 easily escapes to reach an equilibrium state, and a low-temperature end of the sample 250 can be formed. As a result, a temperature gradient is formed between both ends of the sample 250 . In addition, since the copper blocks 210 and 220 have excellent electrical conductivity, errors in measurement can be minimized.

After generating a temperature gradient at both ends of the sample 250 , the temperature of each end, and the temperature gradient and voltage generated at both ends were simultaneously measured using a multimeter 230 . At this time, a change in the Seebeck coefficient was measured while irradiating light using a light source 260 such as a UV LED.

6 is a graph showing the absorbance of ZnO and the absorbance of Ag nanoparticles by increased Ag nanoparticles. The horizontal axis is wavelength (nm) and the vertical axis is absorption (absorbance, a.u.).

When looking at the absorbance (ZnO in FIG. 6) of the sample made of only ZnO, which is a comparative example, it can be seen that almost no absorption is achieved for a wavelength of 425 nm or more. A strong peak is observed between 400 nm and 500 nm in the absorbance of Ag nanoparticles (Ag NPs in FIG. 6). The ZnO sample (ZnO + Ag NP in FIG. 6) complexed with Ag nanoparticles according to the present invention exhibits high absorbance even at a wavelength of 400 nm or more due to the effect of Ag nanoparticles.

7 is a SEM image of Ag nanoparticles deposited on a ZnO thin film according to the present invention. Ag nanoparticles formed by deposition on the ZnO thin film had an average size of 18 nm, and it was confirmed that they occupied 35% of the total area of the thin film.

8 is a graph showing a change in the Seebeck coefficient according to the time when light is irradiated in the experimental examples.

)이다. 빛을 쪼이기 전, 쪼이는 동안, 빛을 끈 다음의 제벡계수가 시간순으로 나타나 있다. 8(a) is when green light is irradiated in Comparative Example, (b) is when blue light is irradiated in Comparative Example, (c) is when green light is irradiated in Example, (d) is when blue light is irradiated in Example is the result of In the graph, the horizontal axis is time (time, sec) and the vertical axis is the Seebeck coefficient (

)am. The Seebeck coefficients before, during, and after the light is turned off are shown in chronological order.

Referring to FIG. 8 , as in (c) and (d), the increase in Seebeck coefficient increases when green and blue light is irradiated after deposition of Ag nanoparticles on ZnO.

In the light of the wavelength band of blue light (425 nm), it can be seen that the Seebeck coefficient of ZnO increases regardless of the presence or absence of Ag nanoparticles. However, when irradiated with green light (520 nm), an increase in the Seebeck coefficient is confirmed only in the sample sample in which Ag nanoparticles are deposited as in the present invention.

증가하였다. 또한 Ag 나노입자가 증착되지 않은 비교예 ZnO 샘플의 경우 425nm 파장의 빛에서 최대 0.3

의 제백계수의 증가가 확인되었지만 빛에 대한 반응의 속도가 매우 느리게 일어났고 빛을 비추지 않은 상태와 차이가 명확하게 나타나지 않았다. 하지만, Ag 나노입자가 증착된 실시예 ZnO 샘플의 경우 0.3

의 제백계수의 증가가 확인되었고 빛을 비추지 않은 상태와 차이가 명확하게 나타난다. 이러한 부분에서 빛에 의한 효과가 Ag 나노입자가 증착된 샘플의 경우 플라즈모닉 공명에 의한 흡광 증폭으로 인해 더 명확하게 나타나고 제백효과 효율이 더 증가되었다고 볼 수 있다.The comparative example ZnO sample in which Ag nanoparticles were not deposited did not respond to light at a wavelength of 520 nm, whereas, in the case of the Example ZnO sample in which Ag nanoparticles were deposited, the Seebeck coefficient was at most 0.2.

increased. In addition, in the case of the comparative ZnO sample in which Ag nanoparticles were not deposited, a maximum of 0.3 in light of a wavelength of 425 nm

Although the increase of the Seebeck coefficient was confirmed, the rate of reaction to light was very slow, and the difference with the state without light was not clearly seen. However, for the example ZnO sample on which Ag nanoparticles were deposited, 0.3

An increase in the Seebeck coefficient of . In this part, it can be seen that the effect of light appeared more clearly due to absorption amplification by plasmonic resonance in the case of the sample on which Ag nanoparticles were deposited, and the Seebeck effect efficiency was further increased.

As such, ZnO, which showed an increase in the Seebeck coefficient due to light only in the region of less than 425 nm, increased in the wider wavelength band of 520 nm or more due to Ag nanoparticles. This is clearly the result of the absorption area expansion and absorption amplification of the visible light by plasmonic resonance by Ag nanoparticles.

The Seebeck coefficient is increased due to charge injection by light at the moment of illuminating the light. The maintenance of the increase of the Seebeck coefficient through the light in the visible region lasts for a short time unit of seconds. In order to use the increased Seebeck coefficient as an actual thermoelectric element, it is preferable to operate in sunlight to illuminate the light or to further provide a means for illuminating the light.

As described above, although the present invention has been described with reference to limited embodiments and drawings, the present invention is not limited thereto, and the technical idea of the present invention and the following by those skilled in the art to which the present invention pertains. It goes without saying that various modifications and variations are possible within the scope of equivalents of the claims to be described.

100: thermoelectric material
110: ZnO base
120: Ag nanoparticles

Claims (7)

ZnO substrate made of thin or thick film or bulk material made of ZnO; and
Ag nanoparticles formed on the surface of the ZnO substrate,
A charge trap exists due to the discontinuity of the bond present at the interface between the ZnO substrate and the Ag nanoparticles,
Thermoelectric material, characterized in that the Ag nanoparticles absorb light to cause absorption amplification by surface plasmonic resonance to increase the Seebeck coefficient of the ZnO. The thermoelectric material according to claim 1, wherein the concentration of free electrons increases by excitation of electrons in response to light having a wavelength exceeding 425 nm. The thermoelectric material according to claim 1, wherein the thermoelectric material operates in sunlight or further includes a means for illuminating the thermoelectric material. A method for manufacturing the thermoelectric material according to claim 1, comprising:
Preparing a ZnO substrate made of a thin or thick film or bulk material made of ZnO; and
and forming Ag nanoparticles on the surface of the ZnO substrate. The method of claim 4, wherein the manufacturing of the ZnO substrate comprises:
preparing a Zn source solution;
forming a ZnO thin film by applying the Zn source solution; and
Thermoelectric material manufacturing method comprising the step of heat-treating the ZnO thin film. The method according to claim 5, wherein the Zn source solution is prepared by stirring zinc acetate (Zinc-acetate) in a solution of methoxyethanol (2-Methoxyethalnol) mixed with ethanolamine (Ethanolamine). . The method of claim 4, wherein the forming of the Ag nanoparticles comprises:
A method for manufacturing a thermoelectric material, characterized in that Ag nanoparticles are formed by depositing Ag in a thermal evaporator.

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