A method for predicting the long-term service performance of thermoelectric devices and its application

Abstract

The present invention relates to a method and application for predicting the long-term service performance of thermoelectric devices. The method comprises: experimentally obtaining data on the sublimation kinetics of thermoelectric materials, the thickening kinetics of the reaction layer at the thermoelectric material / electrode interface, and the interface resistivity of the thermoelectric material / electrode interface; establishing a control boundary equation between the thermoelectric arm substrate and the sublimation decomposition layer at the thermoelectric material surface, and obtaining the parameter coordinates of the control boundary under a given thermoelectric material and service temperature; constructing a geometric model based on the control equation for the boundary between the thermoelectric arm substrate and the decomposition layer, taking into account the temperature dependence of material physical properties; setting the interface resistivity in the electric field based on the relationship between the interface resistivity and temperature and time; varying the parameters, and performing numerical calculations using the thermoelectric effect physical field of simulation software to obtain predicted values for the long-term service performance of the thermoelectric device at different service temperatures. According to the present invention, long-term service performance prediction of the device can be achieved based on the performance decay of the thermoelectric material.

Description

Technical Field

[0001] The present invention relates to the technical field of thermoelectric materials and devices, and in particular to a method for predicting the long-term service performance of a thermoelectric device and its application. Background Art

[0002] The rapid development of human society has dramatically increased the demand for energy. To alleviate the growing shortage of fossil fuels and the deteriorating environment, new, efficient, and pollution-free energy technologies are needed. Thermoelectric conversion technology based on the Seebeck effect offers advantages such as compact size, noiselessness, and environmental friendliness. It has broad application prospects in industrial waste heat recovery, passive sensors, and space power sources, and has become a research hotspot in materials science in recent years.

[0003] For years, researchers have been working to improve the energy conversion efficiency of thermoelectric devices. The conversion efficiency of single-stage skutterudite-based thermoelectric devices has reached 10%, while the conversion efficiency of bismuth telluride-skutterudite- and bismuth telluride-half-Heusler-based dual-stage thermoelectric devices has exceeded 12%. In addition to pursuing high energy conversion efficiency, the service performance of thermoelectric devices is also crucial. Thermoelectric devices typically operate for long periods at high temperatures and large temperature gradients. This inevitably leads to diffusion and chemical reactions at the interface between the thermoelectric legs and the electrodes, as well as sublimation of volatile elements on the thermoelectric material surface. This increases the device's internal resistance and reduces the open-circuit voltage, output power, and conversion efficiency. The introduction of diffusion barriers can only reduce the diffusion rate at the electrode interface but cannot completely inhibit diffusion. Surface coatings on thermoelectric materials can only reduce the sublimation rate but cannot completely prevent it. Therefore, performance degradation of thermoelectric devices over long periods of service is inevitable. The surface and interface behaviors involved in this degradation are complex and difficult to quantitatively describe, and there are no models or methods to predict long-term service performance.

[0004] Chu et al. (Nature Communication, 2020, 11 (1)) studied the interfacial service behavior of skutterudite-based thermoelectric materials, and used the diffusion-reaction model and Arrhenius formula to describe the kinetic process of the interfacial reaction. They found that the increase in interfacial resistivity is proportional to the increase in the thickness of the interfacial reaction layer, and the change in interfacial resistivity over time can be predicted. In addition, the sublimation of Sb elements on the surface of skutterudite-based thermoelectric materials causes a large number of pores on the surface of the material, thereby reducing the electrical and thermal properties of the material. Zhao et al. experimentally studied the sublimation weight loss behavior of Sb at different temperatures in CoSb3 (Journal of Alloys and Compounds, 2011, 509 (6): 3166-3171), and used the Arrhenius formula to describe the sublimation kinetics. However, the above results only remain at the material level or component level, and can only qualitatively describe the long-term service performance of thermoelectric devices, but cannot be quantitatively linked to the long-term service performance of thermoelectric devices, resulting in the current inability to effectively predict the attenuation of the long-term service performance of thermoelectric devices. At the device level, Yatir Sadia et al. (Physical Chemistry Chemical Physics, 2017, 19 (29): 19326-19333) measured the performance changes of PbTe-based materials after isothermal aging and the corresponding thermoelectric devices after temperature differential service, and obtained the performance of materials with different aging times at 520°C and the service performance of thermoelectric devices at a temperature difference of 60°C-600°C, as well as the morphology of the thermoelectric arm cross section. The device performance was predicted using the changes in the base material properties and morphology. The changes in morphology in this method are not predictive, and the prediction of device performance is based on the performance test of the corresponding aging time of the material, which is unrealistic for long-term prediction. For the prediction of radioisotope thermoelectric generator (RTG) performance, Thomas E. Hammel proposed a hybrid model (7th International Energy Conversion Engineering Conference, 2-5 August, 2009: 4576). The model uses polynomials to fit the measured service data of the internal resistance and open circuit voltage of the RTG, and combines the attenuation of the heat source temperature to make an extrapolated prediction. Christofer E. Whiting proposed a method for fitting the rate equation (Nuclear Technology, 2021, 207 (6): 782-789), using Mathematical fitting of the RTG's output power yields good prediction results. The two aforementioned methods can effectively predict the long-term service performance of RTGs, but the models are based on the fitting and extrapolation of a large amount of long-term service performance experimental data, lack predictability, and the attenuation mechanism and laws are unclear, making them difficult to apply to thermoelectric devices of other material systems. Therefore, there is an urgent need to establish a model that predicts the long-term performance of thermoelectric devices at different service temperatures based on the study of the surface and interface behavior of thermoelectric materials or thermoelectric elements. This model will provide a theoretical basis for the evolution of the long-term service performance of thermoelectric devices, accurately predict the service performance of the devices, and optimize the structural design and service conditions of thermoelectric devices. Summary of the Invention

[0005] Problems to be solved by the invention:

[0006] In response to the problem that the long-term service performance of thermoelectric materials and devices is difficult to quantitatively describe as described above, the purpose of the present invention is to provide a method and application for predicting the long-term service performance of thermoelectric devices based on the attenuation of thermoelectric material performance to achieve device long-term service performance prediction.

[0007] Technical means to solve the problem:

[0008] The present invention provides a method for predicting the long-term service performance of a thermoelectric device, comprising:

[0009] Through experiments, we obtain the surface sublimation kinetics data of thermoelectric materials, the thickening kinetics data of the reaction layer at the thermoelectric material / electrode interface, and the interface resistivity data of the thermoelectric material / electrode interface;

[0010] The control boundary equation of the thermoelectric arm substrate and the sublimation decomposition layer on the surface of the thermoelectric material is established as follows: y = d - f 1( T , t ), under certain thermoelectric materials and service temperatures, the temperature distribution in the thermoelectric arm is T = g ( y ), the parameter coordinates of the control boundary line are ( d - f 1( g ( y ), t ), y ),in, d is the vertical distance between the edge of the thermoelectric arm and the center line of the thermoelectric arm, y is the height position of the thermoelectric arm, g The function is obtained by simulation of thermoelectric effect or by linear assumption;

[0011] In combination with the dependence of material physical properties on temperature, a geometric model is constructed based on the boundary line control equation between the thermoelectric arm substrate and the sublimation decomposition layer on the surface of the thermoelectric material. The interface resistivity in the electric field is set based on the relationship between the interface resistivity, temperature and time. By changing the parameters, numerical calculations are performed using the thermoelectric effect physical field of simulation calculation software to obtain the long-term performance prediction values of thermoelectric devices at different service temperatures.

[0012] According to the present invention, experimental data on the sublimation kinetics of the thermoelectric material surface, the thickening kinetics of the thermoelectric material / electrode interface reaction layer, and the interface resistivity data of the corresponding electrode / thermoelectric arm are obtained. The boundary control equation between the thermoelectric arm substrate and the sublimation decomposition layer and the relationship between the change of the interface resistivity with time are established respectively. Combined with numerical simulation software, a sublimation geometric model of the thermoelectric device and a performance prediction physical model are established. Through calculation, the quantitative relationship between the performance parameters such as the internal resistance, open-circuit voltage, and output power of the thermoelectric device and the service temperature and time is obtained, thereby realizing the prediction of the long-term service performance of the thermoelectric device under different service conditions.

[0013] Alternatively, in the present invention,

[0014] When obtaining the surface sublimation kinetics data of thermoelectric materials and the thickening kinetics data of the reaction layer at the thermoelectric material / electrode interface, the pure thermoelectric material block and the thermoelectric element with a barrier layer are cut into particles, vacuum-sealed in a tube, and placed in a tube furnace for aging. After aging, they are cut and polished. The thickness of the sublimation decomposition layer on the surface of the thermoelectric material at different temperatures and times is observed under an electron microscope, and the phase and porosity of the sublimation decomposition layer on the surface of the thermoelectric material are determined. The thickness of the reaction layer at the thermoelectric material / electrode interface is observed, and the interface resistivity of the thermoelectric material / electrode interface is measured.

[0015] Alternatively, in the present invention,

[0016] Thermoelectric material surface sublimation kinetics data is the relationship between the thickness of the sublimation decomposition layer on the surface of the thermoelectric material and the temperature and time. l DL =f 1( T , t ),in, l DL is the thickness of the sublimation decomposition layer on the surface of the thermoelectric material, T is the temperature, t For time.

[0017] Alternatively, in the present invention,

[0018] The kinetic data of the thickening of the thermoelectric material / electrode interface reaction layer is the relationship between the thickness of the thermoelectric material / electrode interface reaction layer and the temperature and time. l IRL =f 2(T , t ),in, l IRL is the thickness of the thermoelectric material / electrode interface reaction layer, T is the temperature, t For time.

[0019] Alternatively, in the present invention,

[0020] The interfacial resistivity of the thermoelectric material / electrode interface under the physical model boundary conditions is ,in a , b It is obtained by linear function fitting based on the interface resistivity of the thermoelectric material / electrode interface and the thickness of the thermoelectric material / electrode interface reaction layer.

[0021] Alternatively, in the present invention,

[0022] The parameters include time t , heat source temperature T h , cold source temperature T c and external resistance value R .

[0023] Alternatively, in the present invention,

[0024] The materials used for the thermoelectric device include but are not limited to one or more of bismuth telluride, skutterudite, half-Heusler alloy, lead telluride, germanium telluride, Zintl phase and silicon-germanium alloy with known thermoelectric properties.

[0025] Alternatively, in the present invention,

[0026] The simulation software includes but is not limited to ANASYS, COMSOL and / or ABAQUS.

[0027] The present invention provides application of the above-mentioned method for predicting the long-term service performance of a thermoelectric device in an oxygen-free / oxygen-containing service process of the thermoelectric device.

[0028] Effects of the invention:

[0029] The present invention can provide a method and application for predicting the long-term service performance of a thermoelectric device, and can realize the long-term service performance prediction of the device based on the performance attenuation of the thermoelectric material. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 The p-type Ce in Example 1 of the present invention is shown 0.9 Fe3CoSb 12 The relationship between the thickness of the decomposition layer formed after sublimation of skutterudite material at 600℃, 625℃, 650℃ and 675℃;

[0031] Figure 2 The p-type Ce in Example 1 of the present invention is shown 0.9 Fe3CoSb 12 The relationship between the thickness of the interface reaction layer of the skutterudite component and time at 575℃, 600℃, 625℃ and 650℃;

[0032] Figure 3 The p-type Ce in Example 1 of the present invention is shown 0.9 Fe3CoSb 12 Skutterudite components, electrodes / Ce 0.9 Fe3CoSb 12 Fitting relationship between interface resistivity and reaction layer thickness;

[0033] Figure 4 The p-type Ce in Example 1 of the present invention is shown 0.9 Fe3CoSb 12 Predicted boundary line and time of thermoelectric arm substrate and thermoelectric arm decomposition layer of skutterudite single-leg device under the conditions of heat source temperature 600℃ and cooling source temperature 27℃ t relationship;

[0034] Figure 5 The p-type Ce in Example 1 of the present invention is shown 0.9 Fe3CoSb 12 The internal resistance of the thermoelectric device is 27°C when the heat source temperature is 625°C, 600°C and 550°C respectively and the cold source temperature is fixed at 27°C. R in , open circuit voltage V oc and maximum output power P max Predicted curve of parameter changes over time, and compared with the measured performance after 15 days of service under the conditions of heat source temperature of 625℃ and cold source temperature of 27℃;

[0035] Figure 6 The n-type Yb 0.3 Co4Sb 12 The relationship between the thickness of the decomposition layer formed after sublimation of skutterudite material at 600℃, 625℃, 650℃ and 675℃;

[0036] Figure 7 The n-type Yb 0.3 Co4Sb 12 The relationship between the thickness of the interface reaction layer of the skutterudite component and time at 575℃, 600℃, 625℃ and 650℃;

[0037] Figure 8 The n-type Yb0.3 Co4Sb 12 Skutterudite components, electrodes / Yb 0.3 Co4Sb 12 Fitting relationship between interface resistivity and reaction layer thickness;

[0038] Figure 9 The n-type Yb 0.3 Co4Sb 12 Predicted boundary line and time of thermoelectric arm substrate and thermoelectric arm decomposition layer of skutterudite single-leg device under the conditions of heat source temperature 600℃ and cooling source temperature 27℃ t relationship;

[0039] Figure 10 The n-type Yb 0.3 Co4Sb 12 The internal resistance of the thermoelectric device is 27°C when the heat source temperature is 650°C, 600°C and 550°C respectively and the cold source temperature is fixed at 27°C. R in , open circuit voltage V oc and maximum output power P max Prediction curve of parameter changes over time, and comparison with the measured performance after 15 days of service under the conditions of heat source temperature of 650℃ and cold source temperature of 27℃;

[0040] Figure 11 The p-type Nb in Example 3 of the present invention is shown. 0.86 Hf 0.14 The thickness of the decomposition layer formed after sublimation of FeSb half-Heusler material at 800℃, 825℃, 850℃ and 875℃ as a function of time;

[0041] Figure 12 The p-type Nb in Example 3 of the present invention is shown. 0.86 Hf 0.14 The relationship between the thickness of the interface reaction layer of FeSb half-Heusler element and time at 800℃, 825℃, 850℃ and 875℃;

[0042] Figure 13 The p-type Nb in Example 3 of the present invention is shown. 0.86 Hf 0.14 FeSb half-Heusler element, electrode / Nb 0.86 Hf 0.14 Fitting relationship between FeSb interface resistivity and reaction layer thickness;

[0043] Figure 14 The p-type Nb in Example 3 of the present invention is shown. 0.86 Hf 0.14The predicted boundary line and time of the thermoelectric arm substrate and thermoelectric arm decomposition layer of the FeSb half-Heusler single-leg device under the conditions of heat source temperature 850℃ and cold source temperature 27℃ t relationship;

[0044] Figure 15 The p-type Nb in Example 3 of the present invention is shown. 0.86 Hf 0.14 The internal resistance of the FeSb half-Heusler device is 2.33 V under the conditions of heat source temperature of 900℃, 850℃ and 800℃ and cold source temperature of 27℃. R in , open circuit voltage V oc and maximum output power P max Prediction curve of parameter changes over time. DETAILED DESCRIPTION

[0045] The present invention is further described below in conjunction with the following embodiments. It should be understood that the following embodiments are only used to illustrate the present invention, not to limit the present invention. The same or corresponding reference numerals in the figures represent the same components, and repeated descriptions are omitted. The components of the embodiments of the present invention generally described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0046] The present invention also provides a method for predicting the long-term service performance of thermoelectric devices. The method comprises aging a thermoelectric material block and a thermoelectric element with a barrier layer to obtain surface sublimation kinetic data of the thermoelectric material, thickening kinetic data of the thermoelectric material / electrode interface reaction layer, and corresponding thermoelectric material / electrode interface resistivity data. The method then establishes a governing equation for the boundary between the thermoelectric arm substrate and the sublimation decomposition layer (sometimes referred to as the decomposition layer) on the surface of the thermoelectric material, and a time-dependent relationship between the interface resistance (sometimes also referred to as the contact resistance). Numerical simulation software is then used to establish a sublimation geometric model and a performance prediction physical model for the thermoelectric device. The method then calculates the quantitative relationship between performance parameters such as the thermoelectric device's internal resistance, open-circuit voltage, and output power and the service temperature and time, thereby enabling prediction of the long-term service performance of the thermoelectric device under different service conditions.

[0047] Specifically, we first obtain the surface sublimation kinetics data of thermoelectric materials and the thickening kinetics data of the thermoelectric material / electrode interface reaction layer through experiments.

[0048] The thermoelectric element with electrodes is cut into particles, sealed in a vacuum tube, and aged in a tube furnace at no fewer than three aging temperatures and no fewer than five aging times at each temperature. After aging, the sample is cut and polished. The thickness of the sublimation decomposition layer on the thermoelectric material surface is observed under an electron microscope at different temperatures and times to determine the phase and porosity of the sublimation decomposition layer. The thickness of the reaction layer at the thermoelectric material / electrode interface (sometimes referred to as the reaction layer) is also observed, and the interfacial resistivity of the thermoelectric material / electrode interface is measured.

[0049] In the present invention, the sublimation kinetics data of the thermoelectric material surface is the relationship between the thickness of the sublimation decomposition layer on the thermoelectric material surface and the temperature and time. The thickness of the sublimation decomposition layer on the thermoelectric material surface under any temperature and time parameters is obtained by fitting the Arrhenius formula. l DL =f 1( T , t ),in, T is the temperature, t In the present invention, the thickening kinetic data of the thermoelectric material / electrode interface reaction layer is the relationship between the thickness of the thermoelectric material / electrode interface reaction layer and the temperature and time. The thickness of the thermoelectric material / electrode interface reaction layer under any temperature parameter and time parameter is obtained by combining the interface diffusion reaction equation and the Arrhenius formula. l IRL =f 2 (T, t) ,in, T is the temperature, t For time.

[0050] In addition, the thickness of the thermoelectric material / electrode interface reaction layer affects the interface resistivity. By measuring the interface resistivity of the thermoelectric material / electrode interface, the interface resistivity at different temperatures and times under the boundary conditions of the physical model can be established. ,in a , b It is obtained by linear function fitting based on the interface resistivity of the thermoelectric material / electrode interface and the thickness of the thermoelectric material / electrode interface reaction layer.

[0051] In addition, the surface sublimation of the thermoelectric material affects the geometric dimensions of the thermoelectric arm substrate and the decomposition layer. In the geometric model, the thermoelectric arm consists of the thermoelectric arm substrate and the thermoelectric material surface sublimation decomposition layer. Therefore, the boundary line control equation between the thermoelectric arm substrate and the thermoelectric material surface sublimation decomposition layer is: y = d - f 1( T , t ),in, y is the height position of the thermoelectric arm, dis the vertical distance between the edge of the thermoelectric arm and the center line of the thermoelectric arm, T is the temperature, t The structural parameters are based on the control boundary equation between the thermoelectric arm matrix of the thermoelectric material and the sublimation decomposition layer on the surface of the thermoelectric material. Under certain thermoelectric materials and service temperatures, the temperature distribution in the thermoelectric arm is expressed as T = g ( y ),in g The function can be obtained through thermoelectric effect simulation or linear assumption, and the parameter coordinates of the control boundary line are ( d - f 1( g ( y ), t ), y ),in, d is the vertical distance between the edge of the thermoelectric arm and the center line of the thermoelectric arm, y is the height position of the thermoelectric arm, g ( y ) is the relationship between temperature and the height position of the thermoelectric arm.

[0052] Next, numerical calculations are performed using the thermoelectric effect physical field of commercial simulation software, taking into account the dependence of material physical parameters on temperature. As mentioned above, the construction of the geometric model is based on the relationship between the geometric structure of the thermoelectric arm matrix and the sublimation decomposition layer on the surface of the thermoelectric material and time and temperature, and the setting of the interface resistivity in the electric field is based on the relationship between the interface resistivity of the thermoelectric material / electrode interface and temperature and time. By changing the parameters for thermoelectric simulation calculations, the relationship between the internal resistance, open circuit voltage and maximum output power of the thermoelectric device and time at different service temperatures can be obtained, thereby achieving the prediction of the long-term performance of the thermoelectric device. This parameter includes but is not limited to time t , heat source temperature T h , cold source temperature T c and external resistance value R。 Different service temperatures include, for example, the temperatures of the high-temperature end and the low-temperature end of different thermoelectric devices.

[0053] In addition, the materials used in the thermoelectric device of the present invention include but are not limited to bismuth telluride, skutterudite, half-Heusler alloy, lead telluride, germanium telluride, Zintl phase and silicon-germanium alloy with known thermoelectric properties. In addition, the present invention adopts finite element calculation method, and the calculation software that can be used includes but is not limited to commercial simulation software such as ANASYS, COMSOL and ABAQUS. The physical field used in the numerical simulation calculation model can be the thermoelectric effect physical field. In addition, in the present invention, the above l DL =f 1( T , t), l IRL =f 2( T , t ), The specific relationships can be obtained through experiments.

[0054] Based on the above, the present invention establishes the governing equations for the boundary between the thermoelectric arm substrate and the sublimation decomposition layer, and the temporal relationship between the interface resistivity, based on the surface sublimation kinetics of the thermoelectric material, the thickening kinetics of the reaction layer between the thermoelectric arm and the electrode, and the corresponding thermoelectric material / electrode interface resistivity data. Furthermore, numerical simulation software is used to establish a sublimation geometry model and a performance prediction physical model for the thermoelectric device, thereby enabling prediction of the long-term performance of thermoelectric materials and devices and guiding the optimization of the device geometry and service conditions. The method for predicting the long-term service performance of thermoelectric devices described in the present invention has a variety of applications, such as application in the oxygen-free and oxygen-containing service processes of thermoelectric devices.

[0055] The following examples are further listed to illustrate the present invention in detail. It should be understood that the following examples are only used to illustrate the present invention in detail and should not be understood as limiting the scope of protection of the present invention.

[0056] Example 1

[0057] This embodiment is p-type Ce 0.9 Fe3CoSb 12 The method for predicting the long-term service performance of skutterudite devices includes the following steps:

[0058] 1. Separately, pure Ce 0.9 Fe3CoSb 12 The material block and the thermoelectric element with Nb barrier layer are cut into particles, vacuum sealed in a tube, and placed in a tube furnace for aging; pure Ce 0.9 Fe3CoSb 12 The aging temperature points of the material block are 600℃, 625℃, 650℃ and 675℃, the aging time points at 600℃ are 2 days, 4 days, 7 days, 12 days and 15 days, the aging time points at 625℃ are 2 days, 4 days, 6 days, 9 days and 12 days, the aging time points at 650℃ are 2 days, 4 days, 6 days, 8 days and 10 days, and the aging time points at 675℃ are 1 day, 2 days, 3 days, 5 days and 7 days. The aging temperature points of the thermoelectric elements with Nb barrier layer are 575℃, 600℃, 625℃ and 650℃, the aging time points at 575℃ are 3 days, 6 days, 9 days, 12 days and 15 days, the aging time points at 600℃ are 2 days, 4 days, 6.5 days, 8 days and 11 days, the aging time points at 625℃ are 1 day, 2 days, 3 days, 4 days and 5 days, and the aging time points at 650℃ are 0.5 day, 1 day, 2 days, 3 days and 4 days.

[0059] 2. After aging, cut and polish the sample and observe Ce under an electron microscope. 0.9 Fe3CoSb 12 The surface sublimation layer was determined by EDS to be the main component of the matrix phase Ce. 0.9 Fe3CoSb 12 , the porosity is about 20%. At temperatures of 600℃, 625℃, 650℃ and 675℃, the relationship between the thickness of the sublimation decomposition layer on the surface of the thermoelectric material and time is as follows Figure 1 As shown; at temperatures of 575℃, 600℃, 625℃ and 650℃, electrode / Ce 0.9 Fe3CoSb 12 The relationship between the thickness of the interface reaction layer and time is as follows: Figure 2 Measuring electrode / Ce 0.9 Fe3CoSb 12 The contact resistivity of the interface, the relationship between the contact resistivity and the thickness of the reaction layer at 600℃ is as follows Figure 3 shown.

[0060] 3. The thickness of the sublimation decomposition layer under arbitrary temperature and time parameters is obtained by fitting the Arrhenius formula. The Ce 0.9 Fe3CoSb 12 The relationship equation between the thickness of the material sublimation decomposition layer and temperature and time is:

[0061] ;in, l DL is the thickness of the decomposition layer, in mm; T is the temperature in K; t is the time in days. Combining the interface diffusion reaction equation and the Arrhenius formula to fit the interface reaction layer thickness under arbitrary temperature parameters and time parameters, the Ce obtained by fitting is 0.9 Fe3CoSb 12 The relationship equation between the thickness of the interface reaction layer between the material and the Nb barrier layer and temperature and time is:

[0062] ;in, l IRL is the thickness of the reaction layer, in m; T is the temperature in K; t is the time in days. The fitting relationship between contact resistivity and reaction layer thickness is: , unit μΩ·cm 2 .

[0063] 4. Use commercial simulation software to perform numerical calculations on the thermoelectric effect physical field. The commercial simulation software selected is COMSOL. The required materials include electrodes, ceramic plates, barrier materials, thermoelectric materials Ce 0.9 Fe3CoSb 12 , physical properties of the sublimation decomposition layer material, including electrical conductivity, thermal conductivity, and Seebeck coefficient. Temperature dependence is considered when setting material property parameters. The geometric model is constructed based on the relationship between the geometric structure of the thermoelectric arm substrate and decomposition layer and time and temperature. The thermoelectric arm is a φ6*10mm cylinder. Therefore, the horizontal coordinate of the boundary between the thermoelectric arm substrate and the decomposition layer, centered at the bottom of the thermoelectric arm centerline, is:

[0064] ;in, T is the temperature in K; t The temperature distribution in the thermoelectric arm is linear. When the high temperature end is 898K and the low temperature end is 300K, the function T =59.8 y +300, the unit is K, where y is the vertical coordinate of the dividing line with the lowest end of the center line of the thermoelectric arm as the center. The parameter equation for controlling the dividing line is:

[0065] ;

[0066] p-type Ce 0.9 Fe3CoSb 12 Predicted boundary line and time of thermoelectric arm substrate and thermoelectric arm decomposition layer under the conditions of heat source temperature 600℃ and cooling source temperature 27℃ for skutterudite device t The relationship as Figure 4 shown.

[0067] 5. Set the thermal boundary and current boundary conditions of the model. The contact resistivity between the thermoelectric arm and the barrier layer is set to:

[0068] ; The unit is μΩ·cm 2 .

[0069] 6. By changing parameters, including time t , heat source temperature T h and cold source temperature T c By performing thermoelectric simulation calculations, we can obtain the relationship between the internal resistance, open circuit voltage and maximum output power over time at different service temperatures and compare them with the actual test results, such as Figure 5 shown.

[0070] Example 2

[0071] In this embodiment, n-type Yb 0.3 Co4Sb 12 The method for predicting the long-term service performance of skutterudite devices includes the following steps:

[0072] 1. Separately, pure Yb 0.3 Co4Sb 12 The material block and the thermoelectric element with Nb barrier layer are cut into particles, vacuum sealed in a tube, and placed in a tube furnace for aging; pure Yb 0.3 Co4Sb 12 The aging temperature points of the material block are 600℃, 625℃, 650℃ and 675℃, the aging time points at 600℃ are 2 days, 4 days, 7 days, 12 days and 15 days, the aging time points at 625℃ are 2 days, 4 days, 6 days, 9 days and 12 days, the aging time points at 650℃ are 2 days, 4 days, 6 days, 8 days and 10 days, and the aging time points at 675℃ are 1 day, 2 days, 3 days, 5 days and 7 days. The aging temperature points of the thermoelectric elements with Nb barrier layer are 575℃, 600℃, 625℃ and 650℃, the aging time points at 575℃ are 3 days, 6 days, 9 days, 12 days and 15 days, the aging time points at 600℃ are 2 days, 4 days, 6.5 days, 8 days and 11 days, the aging time points at 625℃ are 1 day, 2 days, 3 days, 4 days and 5 days, and the aging time points at 650℃ are 0.5 day, 1 day, 2 days, 3 days and 4 days.

[0073] 2. After aging, cut and polish the sample and observe Yb under electron microscope. 0.3 Co4Sb 12 The surface sublimation layer is determined by EDS, and the main component of the sublimation layer is the matrix phase CoSb2, with a porosity of about 15%. At temperatures of 600℃, 625℃, 650℃ and 675℃, the relationship between the thickness of the sublimation decomposition layer on the surface of the thermoelectric material and time is as follows: Figure 6 As shown; at temperatures of 575℃, 600℃, 625℃ and 650℃, the electrode / Yb 0.3 Co4Sb 12 The relationship between the thickness of the interface reaction layer and time is as follows: Figure 7 As shown, the measuring electrode / Yb 0.3 Co4Sb 12 The contact resistivity of the interface, the relationship between the contact resistivity and the thickness of the reaction layer at 600℃ is as follows Figure 8 shown.

[0074] 3. The thickness of the sublimation decomposition layer under arbitrary temperature and time parameters is obtained by fitting the Arrhenius formula. The Yb 0.3 Co4Sb 12 The relationship equation between the thickness of the material sublimation decomposition layer and temperature and time is:

[0075] ;in, l DL is the thickness of the decomposition layer, in mm; T is the temperature in K; t is the time in days. Combining the interface diffusion reaction equation and the Arrhenius formula to fit the interface reaction layer thickness under arbitrary temperature parameters and time parameters, the Yb 0.3 Co4Sb 12 The relationship equation between the thickness of the interface reaction layer between the material and the Nb barrier layer and temperature and time is:

[0076] ;in, l IRL is the thickness of the reaction layer, in m; T is the temperature in K; t is the time in days. The fitting relationship between contact resistivity and reaction layer thickness is: , unit μΩ·cm 2 .

[0077] 4. Use commercial simulation software to perform numerical calculations on the thermoelectric effect physical field. The commercial simulation software selected is COMSOL. The required materials include electrodes, ceramic plates, barrier materials, and thermoelectric material Yb 0.3 Co4Sb 12 , physical properties of the sublimation decomposition layer material, including electrical conductivity, thermal conductivity, and Seebeck coefficient. Temperature dependence is considered when setting material property parameters. The geometric model is constructed based on the relationship between the geometric structure of the thermoelectric arm substrate and decomposition layer and time and temperature. The thermoelectric arm is a φ6*10mm cylinder. Therefore, the horizontal coordinate of the boundary between the thermoelectric arm substrate and the decomposition layer, centered at the bottom of the thermoelectric arm centerline, is:

[0078] ;in, T is the temperature in K; t The temperature distribution in the thermoelectric arm is linear. When the high temperature end is 898K and the low temperature end is 300K, the function T =59.8 y +300, the unit is K, where y is the vertical coordinate of the dividing line with the lowest end of the center line of the thermoelectric arm as the center. The parameter equation for controlling the dividing line is:

[0079] n-type Yb 0.3 Co4Sb 12 When the heat source temperature is 600℃ and the cooling source temperature is 27℃, the relationship between the predicted boundary line between the thermoelectric arm substrate and the thermoelectric arm decomposition layer and time t is as follows: Figure 9 shown.

[0080] 5. Set the thermal boundary and current boundary conditions of the model. The contact resistivity between the thermoelectric arm and the barrier layer is set to:

[0081] ; The unit is μΩ·cm 2 。

[0082] 6. By changing parameters, including time t , heat source temperature T h and cold source temperature T c By performing thermoelectric simulation calculations, we can obtain the relationship between the internal resistance, open circuit voltage and maximum output power over time at different service temperatures and compare them with the actual test results, such as Figure 10 shown.

[0083] Example 3

[0084] In this embodiment, p-type Nb 0.86 Hf 0.14 The method for predicting the long-term service performance of FeSb half-Heusler devices includes the following steps:

[0085] 1. Separately, pure Nb 0.86 Hf 0.14 The FeSb material block and the thermoelectric element with Nb barrier layer are cut into particles, vacuum sealed in a tube, and placed in a tube furnace for aging; pure Nb 0.86 Hf 0.14 The aging temperature points of FeSb material blocks are 800℃, 825℃, 850℃ and 875℃, the aging time points at 800℃ are 3 days, 6 days, 9 days, 13 days and 15 days, the aging time points at 825℃ are 2 days, 5 days, 8 days, 11 days and 14 days, the aging time points at 850℃ are 2 days, 5 days, 8 days, 11 days and 14 days, and the aging time points at 875℃ are 2 days, 4 days, 6 days, 9 days and 12 days. The aging temperature points of the thermoelectric element with W barrier layer are 800℃, 825℃, 850℃ and 875℃, the aging time points at 800℃ are 4 days, 9 days, 14 days, 17 days and 20 days, the aging time points at 825℃ are 3 days, 6 days, 9 days, 13 days and 17 days, the aging time points at 850℃ are 3 days, 5 days, 7 days, 10 days and 15 days, and the aging time points at 875℃ are 3 days, 5 days, 7 days, 10 days and 15 days.

[0086] 2. After aging, cut and polish the sample and observe Nb under electron microscope. 0.86 Hf 0.14The sublimation layer on the FeSb surface was determined by EDS to be mainly composed of the matrix phase NbSb2 with a porosity of about 30%. At temperatures of 800°C, 825°C, 850°C and 875°C, the relationship between the thickness of the sublimation decomposition layer on the surface of the thermoelectric material and time is shown in the figure below. Figure 11 As shown; at temperatures of 800℃, 825℃, 850℃ and 875℃, electrode / Nb 0.86 Hf 0.14 The relationship between the thickness of the FeSb interface reaction layer and time is as follows: Figure 12 Measuring electrode / Nb 0.86 Hf 0.14 The contact resistivity of the FeSb interface and the relationship between the contact resistivity and the thickness of the reaction layer at 850°C are as follows: Figure 13 shown.

[0087] 3. The thickness of the sublimation decomposition layer under arbitrary temperature and time parameters is obtained by fitting the Arrhenius formula. The Nb 0.86 Hf 0.14 The relationship between the thickness of the sublimation decomposition layer of FeSb material and temperature and time is as follows:

[0088] ;in, l DL is the thickness of the decomposition layer, in mm; T is the temperature in K; t is the time in days. Combining the interface diffusion reaction equation and the Arrhenius formula to fit the interface reaction layer thickness under arbitrary temperature parameters and time parameters, the Nb 0.86 Hf 0.14 The relationship between the thickness of the interface reaction layer between FeSb material and Nb barrier layer and temperature and time is as follows:

[0089] ;in, l IRL is the thickness of the reaction layer, in m; T is the temperature in K; t is the time in days. The fitting relationship between contact resistivity and reaction layer thickness is: , unit μΩ·cm 2 .

[0090] 4. Use commercial simulation software to perform numerical calculations on the thermoelectric effect physical field. The commercial simulation software is ANSYS Workbench platform. The required materials are electrodes, ceramic plates, barrier materials, thermoelectric materials Nb 0.86 Hf 0.14The physical properties of FeSb and the sublimation decomposition layer include electrical conductivity, thermal conductivity, and Seebeck coefficient. Temperature dependence is considered when setting material property parameters. The geometric model is constructed based on the relationship between the geometric structure of the thermoelectric arm substrate and decomposition layer and time and temperature. The thermoelectric arm is a φ6*10mm cylinder. Therefore, the horizontal coordinate of the boundary between the thermoelectric arm substrate and the decomposition layer, centered at the bottom of the thermoelectric arm centerline, is:

[0091] ;in, T is the temperature in K; t The temperature distribution in the thermoelectric arm is linear. When the temperature at the high end is 1073K and the temperature at the low end is 300K, the function T =77.3· y +300 means, the unit is K, where y is the vertical coordinate of the dividing line with the lowest end of the center line of the thermoelectric arm as the center. Then the parametric equation for controlling the dividing line is:

[0092] p-type Nb 0.86 Hf 0.14 The relationship between the predicted boundary line between the thermoelectric arm substrate and the thermoelectric arm decomposition layer and time t for the FeSb half-Heusler device under the conditions of a heat source temperature of 850℃ and a cold source temperature of 27℃ is as follows: Figure 14 shown.

[0093] 5. Set the thermal boundary and current boundary conditions of the model. The contact resistivity between the thermoelectric arm and the barrier layer is set to:

[0094] ; The unit is μΩ·cm 2 。

[0095] 6. By changing parameters, including time t , heat source temperature T h and cold source temperature T c By performing thermoelectric simulation calculations, we can obtain the relationship between the internal resistance, open circuit voltage and maximum output power over time at different service temperatures, such as Figure 15 shown.

[0096] The above specific embodiments further describe the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not limited to the scope of protection of the present invention. Without departing from the purpose of the basic characteristics of the present invention, the present invention can be embodied in various forms. Therefore, the embodiments of the present invention are used for illustration rather than limitation. Since the scope of the present invention is defined by the claims rather than the specification, and all changes that fall within the scope defined by the claims or the equivalent range of the scope defined by the claims should be understood to be included in the claims. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting the long-term service performance of a thermoelectric device, comprising: Through experiments, we obtain the surface sublimation kinetics data of thermoelectric materials, the thickening kinetics data of the reaction layer at the thermoelectric material / electrode interface, and the interface resistivity data of the thermoelectric material / electrode interface; The control boundary equation of the thermoelectric arm substrate and the sublimation decomposition layer on the surface of the thermoelectric material is established as follows: y = d - f 1( T , t ), under certain thermoelectric materials and service temperatures, the temperature distribution in the thermoelectric arm is T = g ( y ), the parameter coordinates of the control boundary line are ( d - f 1( g ( y ), t ), y ), in, d is the vertical distance between the edge of the thermoelectric arm and the center line of the thermoelectric arm, y is the height position of the thermoelectric arm, g The function is obtained by simulation of thermoelectric effect or by linear assumption; Integrating the temperature dependence of material properties, a geometric model was constructed based on the governing equations for the boundary between the thermoelectric arm substrate and the sublimation decomposition layer on the thermoelectric material surface. The interface resistivity in the electric field was set based on its relationship with temperature and time. By varying the parameters and performing numerical calculations using the thermoelectric effect physics field in commercial simulation software, the long-term performance predictions for thermoelectric devices at different service temperatures were obtained. Thermoelectric material surface sublimation kinetics data is the relationship between the thickness of the sublimation decomposition layer on the surface of the thermoelectric material and the temperature and time. l DL =f 1( T , t ),in, l DL is the thickness of the sublimation decomposition layer on the surface of the thermoelectric material, T is the temperature, t For time; The kinetic data of the thickening of the thermoelectric material / electrode interface reaction layer is the relationship between the thickness of the thermoelectric material / electrode interface reaction layer and the temperature and time. l IRL =f 2( T , t ),in, l IRL is the thickness of the thermoelectric material / electrode interface reaction layer, T is the temperature, t For time; The interfacial resistivity of the thermoelectric material / electrode interface under the physical model boundary conditions is ,in a , b It is obtained by linear function fitting based on the interface resistivity of the thermoelectric material / electrode interface and the thickness of the thermoelectric material / electrode interface reaction layer.

2. The method for predicting the long-term service performance of a thermoelectric device according to claim 1, characterized in that: When obtaining the surface sublimation kinetics data of thermoelectric materials and the thickening kinetics data of the reaction layer at the thermoelectric material / electrode interface, the pure thermoelectric material block and the thermoelectric element with a barrier layer are cut into particles, vacuum-sealed in a tube, and placed in a tube furnace for aging. After aging, they are cut and polished. The thickness of the sublimation decomposition layer on the surface of the thermoelectric material at different temperatures and times is observed under an electron microscope, and the phase and porosity of the sublimation decomposition layer on the surface of the thermoelectric material are determined. The thickness of the reaction layer at the thermoelectric material / electrode interface is observed, and the interface resistivity of the thermoelectric material / electrode interface is measured.

3. The method for predicting the long-term service performance of a thermoelectric device according to claim 1, characterized in that: The parameters include time t , heat source temperature T h , cold source temperature T c and external resistance value R .

4. The method for predicting the long-term service performance of a thermoelectric device according to claim 1, wherein: The materials used for the thermoelectric device include but are not limited to one or more of bismuth telluride, skutterudite, half-Heusler alloy, lead telluride, germanium telluride, Zintl phase and silicon-germanium alloy with known thermoelectric properties.

5. The method for predicting the long-term service performance of a thermoelectric device according to claim 1, wherein: The simulation software includes but is not limited to ANASYS, COMSOL and / or ABAQUS.

6. Application of the method for predicting the long-term service performance of a thermoelectric device according to any one of claims 1 to 5 in an oxygen-free / oxygen-containing service process of the thermoelectric device.

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