A method for screening an indium-containing alloy welding material and an indium-containing alloy welding material

Abstract

This invention relates to the field of screening technology for welding materials, specifically disclosing a method for screening indium-containing alloy welding materials. Based on first-principles calculations using density functional theory, high-precision structural relaxation yields the basic phase information of each crystal structure in the TM1-In-TM2 system. The thermal properties of the binary crystal structure in the TM1-In-TM2 system are calculated. Furthermore, combined with the CALPHAD model, a thermodynamic model of the ternary alloy system is established. The stability and eutectic point of the TM1-In-TM2 system are analyzed, and five low-melting-point eutectic indium-containing alloy welding materials are screened out. Differential scanning calorimetry (DSC) is used to experimentally verify the calculated five ternary alloy systems. The hardness and conductivity of some samples are tested using an HV-1000A microhardness tester and a high-precision Seebeck coefficient and resistivity tester. The results show that the calculated values ​​are in excellent agreement with the experimental values. The proportions of the components of each low-melting-point eutectic indium-containing alloy welding material are discovered for the first time, exhibiting advantages such as low melting point, high powder quality, and no adhesion.

Description

Technical Field

[0001] This invention relates to the field of screening technology for welding materials, specifically to a method for screening indium-containing alloy welding materials and indium-containing alloy welding materials. Background Technology

[0002] In electronic packaging technology, solder alloys, as the connecting materials for electronic devices, are used to form conductive and thermally conductive mechanical connections between the pins of various devices or between circuit wires, ensuring the stable performance of electronic products during service. Therefore, for circuits formed through packaging and assembly, the performance of the solder alloy plays a crucial role in the operation of the entire circuit. Tin-lead solder was once highly regarded in the field of electronic packaging due to its low cost, ease of soldering, and good mechanical and metallurgical properties. Its technology is mature, its applications are widespread, and it has a long history of development. However, because lead (Pb) metal is highly toxic, its use poses significant risks to human health and the environment. Therefore, ceasing the use of tin-lead (Sn-Pb) solder in electronic products has become an inevitable trend in the development of electronic packaging. Since the 1990s, lead-free solder has been a focus of research both domestically and internationally. Currently, common lead-free solders that have been developed and researched include In-Sn, Sn-Ag, Sn-Cu, Sn-Zn, and Sn-Bi.

[0003] Among numerous lead-free solders, In-Sn solders have gained significant development space due to their good plasticity, excellent thermal conductivity, and low melting point. Especially in today's diversified electronic device applications, In-Sn solders can effectively meet various development requirements. However, with the continuous increase in the integration of electronic devices, the challenges to solder joint reliability are also increasing. Adding multiple alloying elements such as Ag, Zn, Cu, and Bi to create multi-element solder alloys can improve alloy performance and enhance solderability. Multi-element alloying is an inevitable trend for new lead-free solder alloys. However, developing new solder alloys is an expensive and time-consuming task; therefore, reducing the development cost and cycle of new solder alloys is an urgent problem to be solved. Summary of the Invention

[0004] One objective of this invention is to provide an efficient method for screening indium-containing alloy welding materials, comprising the following steps:

[0005] Step 1: Obtain the elemental and binary crystal structures present in the TM1-In-TM2 system, where TM1 represents one of Sn and Ag, and TM2 represents one of Sb, Ag, Zn, and Cu.

[0006] Step 2: Optimize the structure of the elemental and binary crystal structures obtained in Step 1, and calculate the formation enthalpy of each elemental and binary crystal structure based on the optimized structure.

[0007] Step 3: Construct an energy convex hull diagram based on the formation enthalpy of each element and each binary crystal structure calculated in Step 2. Analyze the thermodynamic stability of each element and each binary crystal structure based on the constructed energy convex hull diagram.

[0008] Step 4: Based on the quasi-harmonic approximation method, calculate the thermal properties of each binary crystal structure after structural optimization.

[0009] Step 5: Based on the thermal properties of each binary crystal structure calculated in Step 4, and combined with the CALPHAD model, establish a thermodynamic model of the TM1-In-TM2 system, and then obtain the liquid phase projection surface of the TM1-In-TM2 system.

[0010] Step 6: Based on the obtained liquid phase projection surface of the TM1-In-TM2 system, analyze the composition ratio and temperature of the eutectic point, and screen out the corresponding low-melting-point eutectic indium-containing alloy welding materials.

[0011] A preferred embodiment of the present invention is that step 3 includes:

[0012] Step 3.1: Construct energy convex hull diagrams for each binary crystal structure with the enthalpy of formation as the ordinate and the atomic fraction as the abscissa.

[0013] Step 3.2: After constructing the energy convex hull diagrams for each binary crystal structure, the thermodynamic stability of each binary crystal structure is determined based on whether its formation enthalpy is less than 0.0 eV.

[0014] In a preferred embodiment of the present invention, in step 3.2, if the formation enthalpy of the binary crystal structure is greater than 0.0 eV, then the binary crystal structure is thermodynamically unstable; if the formation enthalpy of the binary crystal structure is less than 0.0 eV, but the formation enthalpy of the binary crystal structure does not conform to the rules of the constructed energy convex hull diagram, then the binary crystal structure is not the most stable structure in the TM1-In-TM2 system; if the formation enthalpy of the binary crystal structure is less than 0.0 eV, and the formation enthalpy of the binary crystal structure conforms to the rules of the constructed energy convex hull diagram, then the binary crystal structure is the most stable structure in the TM1-In-TM2 system.

[0015] A preferred embodiment of the present invention is that step 4 includes:

[0016] Step 4.1: Perform phonon spectrum calculations on each of the high-precision optimized binary crystal structures and select binary crystal structures with no imaginary frequencies in their phonon spectra.

[0017] Step 4.2: For each binary crystal structure with no imaginary frequency in the selected phonon spectrum, perform variable volume energy and volume calculations. Specifically, calculate the phonon spectrum of each binary crystal structure with volumes of 0.97, 0.98, 0.99, 1.00, 1.01, 1.02, and 1.03, and obtain the corresponding thermal properties based on the quasi-static approximation method.

[0018] A preferred embodiment of the present invention is that step 4.2 includes: calculating the Helmholtz energy of the thermal properties, and the specific calculation method is as follows:

[0019] The Helmholtz energy is decomposed into three cumulative contributions, as shown in Equation (2):

[0020] F(V,T)=E c (V)+F vib (V,T)+F el (V,T) (2)

[0021] In the formula, F(V,T) represents the Helmholtz energy as a function of temperature T and volume V; E c In the quasi-static approximation method, the directly output 0K static total energy; F vib For vibrational free energy; F el It is the contribution of hot electrons to the Helmholtz energy; F vib (V,T) is calculated from phonon DOS (p-DOS) as follows:

[0022]

[0023] Where K B Where ω is the Boltzmann constant, and g(ω,V) is the phonon density of states, a function of the phonon frequency ω. It is the simplified Planck constant;

[0024] The contribution of hot electron excitation, Fel(V,T), was obtained through MermIn statistical calculation:

[0025] F el (V,T)=E el (V,T)-TS el (V,T) (4)

[0026] Electron entropy S el Calculated using the following formula:

[0027] S el (V,T)=-k B ∫n(ε,V){f(ε,V,T)lnf(ε,V,T)+[1-f(ε,V,T)]ln[1-f(ε,V,T)]}d (5)

[0028] Thermoelectron Energy E el (V,T) is calculated by the following formula:

[0029]

[0030] Where n(ε,V) is the density of electronic states of a single electron with energy ε as a function, f is the Fermi function, and ε F It is Fermi energy.

[0031] In a preferred embodiment of the present invention, step 4.2 further includes:

[0032] The Helmholtz energies at a given temperature for seven given volumes were fitted using the Birch-Murnaghan equation of state, as shown in Equation (7):

[0033] F(V,T)=a+bV -2 / 3 +cV -4 / 3 +dV -2 +eV -8 / 3 (7)

[0034] Where a, b, c, d, and e are fitting parameters; the equilibrium volume Veq(T) and the minimum Helmholtz free energy (F(V)) at a given temperature T are... eq T) is obtained by fitting the following formula:

[0035]

[0036] The equilibrium volume Veq(T) and the coefficient of volumetric thermal expansion (β(T)) are calculated using the following formula:

[0037]

[0038] The relationship between the average linear expansion coefficients α(T) and β(T) is α(T) = β(T) / 3;

[0039] Thermal modulus B T (V,T) is calculated by the following formula:

[0040]

[0041] For the main input data in thermodynamic modeling, the entropy derivation is as follows:

[0042]

[0043] Temperature-dependent enthalpy (H(V) at zero external pressure) eq T) can be calculated using the following formula:

[0044] H(V eq ,T)=U(V eq ,T)=F(V eq,T)+TS(V eq ,T) (12)

[0045] Where U(Veq,T) is the internal energy, and is equal to the isochoric thermal energy (C0). V (V eq The following relationship exists between T and T:

[0046]

[0047] The isobaric heat capacity is obtained from formula (14):

[0048] C P (V eq ,T)=C V (V eq ,T)+V eq TB T (V eq ,T)(β(T)) 2 (14).

[0049] This invention establishes a thermodynamic model of the TM1-In-TM2 system (i.e., a ternary alloy system) using high-throughput first-principles calculations combined with the CALPHAD model, further screening for low-melting-point eutectic indium-containing alloy welding materials. Finally, experiments are conducted to verify the accuracy of the calculations, significantly reducing experimental costs and shortening the product development cycle.

[0050] The second objective of this invention is to provide indium-containing alloy welding materials obtained by the above-described method for screening indium-containing alloy welding materials. Specifically, the screened indium-containing alloy welding materials include those with a Sn:In:Ag ratio of (40.02-45.85):(38.05-43.24):(12.93-16.68) and those with a Sn:In:Zn ratio of (45.02-49.56):(34.47-38.86):(14.36-18.12). One of the following: an indium-containing alloy welding material with a Sn:In:Cu ratio of (46.78-50.92):(44.56-48.32):(3.68-6.76); an indium-containing alloy welding material with an Ag:In:Cu ratio of (7.20-11.40):(80.44-84.56):(6.36-9.66); and an indium-containing alloy welding material with an Ag:In:Sb ratio of (6.85-10.38):(76.56-80.34):(11.64-14.78).

[0051] Compared with other indium-containing alloy welding materials, the low-melting-point indium-containing eutectic welding materials selected by the method of this invention from the Ag-In-Sn, Sn-In-Zn, Ag-In-Cu, Ag-In-Sb, and Sn-In-Cu systems have the following advantages:

[0052] (1) The composition ratio of the low melting point indium-containing eutectic welding material selected is a first discovery.

[0053] (2) The selected low-melting-point indium-containing eutectic welding materials have very low melting points, ranging from 106.04℃ to 143.85℃.

[0054] (3) The calculated values ​​of conductivity and hardness of the selected low-melting-point indium-containing eutectic welding materials are basically consistent with the experimental values.

[0055] (4) The five low-melting-point indium-containing eutectic welding materials selected from the Ag-In-Sb, Sn-In-Zn, Ag-In-Cu, Ag-In-Sb and Sn-In-Cu systems are eutectic alloys. They have no solid-liquid two-phase region, no adhesion phenomenon, are easy to process, and have high powder quality. Attached Figure Description

[0056] Appendix Figure 1 This is a flowchart of the method for screening indium-containing alloy welding materials according to the present invention;

[0057] Appendix Figure 2 The energy convex hull diagram of the Ag-In-Sn system;

[0058] Appendix Figure 3 The energy convex hull diagram of the Sn-In-Cu system;

[0059] Appendix Figure 4 The energy convex hull diagram of the Sn-In-Zn system;

[0060] Appendix Figure 5 The energy convex hull diagram of the Ag-In-Cu system;

[0061] Appendix Figure 6 The energy convex hull diagram of the Ag-In-Sb system;

[0062] Appendix Figure 7 This represents the liquid phase projection surface of the Ag-In-Sn system.

[0063] Appendix Figure 8 This represents the liquid phase projection surface of the Sn-In-Zn system.

[0064] Appendix Figure 9 This represents the liquid phase projection surface of the Ag-In-Cu system.

[0065] Appendix Figure 10 This represents the liquid phase projection surface of the Ag-In-Sb system.

[0066] Appendix Figure 11 This represents the liquid phase projection surface of the Sn-In-Cu system.

[0067] Appendix Figure 12 The electrical conductivity of the Ag-In-Sn system changes with temperature;

[0068] Appendix Figure 13 The electrical conductivity of the Sn-In-Zn system varies with temperature;

[0069] Appendix Figure 14 The conductivity of the Ag-In-Sn system varies with the Ag composition;

[0070] Appendix Figure 15 The conductivity of the Sn-In-Zn system varies with the Zn composition. Detailed Implementation

[0071] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0072] This embodiment describes a method for screening indium-containing alloy welding materials. Based on currently available databases (MaterialsProject, OQMD, SprInger Materials, ICSD, and NIST) and relevant literature reports, it obtains the elemental and binary crystal structures existing in the TM1-In-TM2 system. Here, TM1 represents one of Sn and Ag, and TM2 represents one of Sb, Ag, Zn, and Cu. However, when TM1 represents Ag, TM2 should represent an element other than Ag. The TM1-In-TM2 system refers to a crystal structure containing all three elements: TM1, In, and TM2. Binary crystal structures within the TM1-In-TM2 system refer to binary crystal structures including the TM1-In system, the TM1-TM2 system, and the In-TM2 system.

[0073] A total of 144 crystal structures were obtained, and the basic phase information of each crystal structure was calculated using VASP using a first-principles calculation method based on density functional theory.

[0074] Based on high-throughput first-principles calculations using density functional theory, low-precision and high-precision structure optimizations were performed on 144 crystal structures. The basic phase information of the 144 crystal structures in the TM1-In-TM2 system was obtained, including the lattice constants a, b, c, α, β, γ, space group, volume V, density ρ, and formation enthalpy ΔH of the elemental and binary crystal structures in the TM1-In-TM2 system. The results are shown in Table 1.

[0075] Table 1

[0076]

[0077]

[0078]

[0079]

[0080]

[0081] Energy convex hull diagrams for the Ag-In-Sn, Sn-In-Cu, Sn-In-Zn, Ag-In-Cu, and Ag-In-Sb systems were constructed, as shown in the attached figures. Figure 2 Appendix Figure 3 Appendix Figure 4 Appendix Figure 5 Appendix Figure 6 As shown, the thermodynamic stability of the binary crystal structure in each system is determined.

[0082] Based on the quasi-harmonic approximation (QHA) method, the thermal properties of some elemental and binary crystal structures were calculated. Then, the CALPHAD model parameters were evaluated based on the thermodynamic data obtained from first-principles quasi-harmonic calculations. Finally, thermodynamic models for each system were established, and the liquid phase projection plane of the TM1-In-TM2 system was obtained. The liquid phase projection planes of the Ag-In-Sn, Sn-In-Zn, Ag-In-Cu, Ag-In-Sb, and Sn-In-Cu systems are shown in the attached figures. Figure 7 Appendix Figure 8 Appendix Figure 9 Appendix Figure 10 Appendix Figure 11 As shown. The reliability of the calculation was verified by differential scanning calorimetry (DSC). The conductivity and hardness of the prepared samples were tested using a high-precision Seebeck coefficient and conductivity meter and an HV-1000A microhardness tester. The results show that the calculated values ​​and experimental values ​​are in agreement.

[0083] Compared with other indium-containing alloy welding materials, the low-melting-point indium-containing eutectic welding materials selected through calculation and experimental verification from Ag-In-Sn, Sn-In-Zn, Ag-In-Cu, Ag-In-Sb, and Sn-In-Cu systems have the following advantages:

[0084] (1) The composition ratio of the low melting point indium-containing eutectic welding material selected is a first discovery.

[0085] (2) The low melting point indium-containing eutectic welding materials selected have very low melting points, ranging from 106.04℃ to 143.85℃. Their composition and melting point are shown in Table 2.

[0086] Table 2

[0087]

[0088] (3) The calculated values ​​of electrical conductivity and hardness of the low-melting-point indium-containing eutectic welding materials screened from the Sn-In-Cu, Ag-In-Sb, Sn-In-Zn, Ag-In-Cu and Ag-In-Sb systems are consistent with the experimental values, as shown in Table 3 and Table 4, respectively.

[0089] Table 3

[0090]

[0091]

[0092] Table 4

[0093] serial number Alloy Name Calculated value Experimental value - HBW 1 Sn-In-Cu 11.69 12.00 2 Ag-In-Sb 12.35 12.70 3 Sn-In-Zn 6.39 6.30 4 Ag-In-Cu 10.23 10.42 5 Ag-In-Sb 13.25 13.72

[0094] (4) The five low-melting-point indium-containing eutectic welding materials selected from the Ag-In-Sb, Sn-In-Zn, Ag-In-Cu, Ag-In-Sb and Sn-In-Cu systems are eutectic alloys. They have no solid-liquid two-phase region, no adhesion phenomenon, are easy to process, and have high powder quality.

[0095] The following detailed description of the method for screening indium-containing alloy weldable materials from Ag-In-Sn and Sn-In-Zn systems illustrates the steps of this invention for screening indium-containing alloy weldable materials. The method for screening indium-containing alloy weldable materials from other systems is the same as the screening methods described in Examples 1 and 2 below.

[0096] Example 1

[0097] A method for screening indium-containing alloy welding materials, comprising the following steps:

[0098] Step 1: Based on currently available databases and relevant literature reports, obtain the elemental and binary crystal structures existing in the Ag-In-Sn system, including Sn elemental, In elemental and Ag elemental, as well as In-Sn binary crystal structure, In-Ag binary crystal structure and Sn-Ag binary crystal structure.

[0099] Ag-In-Sn system: refers to a crystal structure containing three elements: Sn, In and Ag. In-Sn binary crystal structure refers to a binary crystal structure containing two elements: In and Sn. In-Ag binary crystal structure refers to a binary crystal structure containing two elements: In and Ag. Sn-Ag binary crystal structure refers to a binary crystal structure containing two elements: Sn and Ag.

[0100] The data paths open in this embodiment include: Materials Project, OQMD, SprInger Materials, ICSD, and NIST.

[0101] Step 2: Optimize the structures of Sn, In, and Ag, as well as the In-Sn, In-Ag, and Sn-Ag binary crystal structures, and calculate the formation enthalpy of Sn, In, Ag, In-Sn, In-Ag, and Sn-Ag binary crystal structures.

[0102] Step 2.1: First, set the parameters "ISIF=3, IBRION=2" to perform low-precision structure optimization on Sn, In, and Ag elements, as well as the In-Sn, In-Ag, and Sn-Ag binary crystal structures. The energy convergence criterion is 10. -6 eV, the convergence criterion for force is The convergence criteria have been met.

[0103] Step 2.2: After the low-precision optimization is completed, high-precision structural optimization is performed again on the low-precision optimized Sn, In, and Ag elements, as well as the In-Sn binary crystal structure, the In-Ag binary crystal structure, and the Sn-Ag binary crystal structure. The energy convergence criterion is 10. -8 eV, the convergence criterion for force is

[0104] Step 2.3: Calculate the formation enthalpy of Sn, In, and Ag elements, as well as the In-Sn binary crystal structure, In-Ag binary crystal structure, and Sn-Ag binary crystal structure, using the formation enthalpy calculation formula. Taking the In-Sn binary crystal structure as an example, the formation enthalpy calculation formula is shown in formula (1):

[0105]

[0106] In the formula: ΔH represents the enthalpy of formation, E total E represents the total energy of the In-Sn binary crystal structure. In and E Sn represents the energy of elemental In and Sn, respectively. x and y represent the number of atoms of elemental In and Sn in the In-Sn binary crystal structure, respectively.

[0107] The formulas for calculating the enthalpy of formation of other binary crystal structures are simply different expressions for the energies of each element. They are in the same form as formula (1), so they will not be repeated here.

[0108] Step 3: Based on the highly optimized Sn, In, and Ag elements, as well as the formation enthalpies of the In-Sn, In-Ag, and Sn-Ag binary crystal structures, construct energy convex hull diagrams. Then, analyze the thermodynamic stability of Sn, In, Ag, and the In-Sn, In-Ag, and Sn-Ag binary crystal structures. Details are as follows:

[0109] Step 3.1: Construct energy convex hull diagrams for the In-Sn binary crystal structure, the In-Ag binary crystal structure, and the Sn-Ag binary crystal structure, respectively, with the enthalpy of formation as the ordinate and the atomic fraction as the abscissa. (See attached diagram.) Figure 2 As shown.

[0110] Taking the Sn-Ag binary crystal structure as an example, an energy convex hull diagram of the Sn-Ag binary crystal structure is constructed using the formation enthalpies of Sn, Sn3Ag, SnAg3 (containing two space groups: Pmmn and P-6m2, i.e., two structures exist) and Ag. As shown in Table 1, Sn, Sn3Ag, SnAg3 (containing two space groups: Pmmn and P-6m2, i.e., two structures exist) and Ag were obtained from the database mentioned above.

[0111] Step 3.2: After constructing the energy convex hull diagrams of the In-Sn binary crystal structure, the In-Ag binary crystal structure, and the Sn-Ag binary crystal structure, determine whether each binary crystal structure is thermodynamically stable based on whether the formation enthalpy of the In-Sn binary crystal structure, the In-Ag binary crystal structure, and the Sn-Ag binary crystal structure is less than 0.0 eV.

[0112] If the formation enthalpy of the binary crystal structure is greater than 0.0 eV, the binary crystal structure is thermodynamically unstable. If the formation enthalpy of the binary crystal structure is less than 0.0 eV, but the formation enthalpy of the binary crystal structure does not conform to the rules of the constructed energy convex hull diagram, then the binary crystal structure is not the most stable structure in the Ag-In-Sn system. If the formation enthalpy of the binary crystal structure conforms to the rules of the constructed energy convex hull diagram, then the binary crystal structure is the most stable structure in the Ag-In-Sn system.

[0113] like Figure 2 As shown, it can be determined that the formation enthalpy of the In-Sn binary crystal structure is greater than 0.0 eV, indicating that it is thermodynamically unstable; there are three most stable binary crystal structures in the In-Ag binary crystal structure, namely In9Ag17, In4Ag9 and InAg3; there is one most stable binary crystal structure in the Sn-Ag binary crystal structure, namely SnAg3.

[0114] Step 4: Based on the first-principles quasi-harmonic approximation method, i.e., the QHA method, the thermal properties of the highly optimized In-Sn binary crystal structure, In-Ag binary crystal structure, and Sn-Ag binary crystal structure are calculated respectively.

[0115] Step 4.1: Phonon spectrum calculations are performed on each of the highly optimized In-Sn binary crystal structure, In-Ag binary crystal structure, and Sn-Ag binary crystal structure using Phonopy software to select In-Sn binary crystal structure, In-Ag binary crystal structure, and Sn-Ag binary crystal structure with no imaginary frequency in the phonon spectrum.

[0116] Step 4.2: Perform variable volume energy and volume calculations on the selected In-Sn binary crystal structures, In-Ag binary crystal structures, and Sn-Ag binary crystal structures with no imaginary frequency in their phonon spectra.

[0117] Specifically, the phonon spectra of In-Sn binary crystal structures, In-Ag binary crystal structures, and Sn-Ag binary crystal structures in volumes of 0.97, 0.98, 0.99, 1.00, 1.01, 1.02, and 1.03 were calculated one by one. The corresponding thermal properties were obtained based on a quasi-static approximation method. The thermal properties described in this embodiment are Helmholtz energies.

[0118] The Helmholtz energy is decomposed into three cumulative contributions, as shown in Equation (2):

[0119] F(V,T)=E c (V)+F vib (V,T)+F el (V,T) (2)

[0120] In the formula, F(V,T) represents the Helmholtz energy as a function of temperature T and volume V; Ec is the total static energy at 0K directly output in the quasi-static approximation method; F vib For vibrational free energy; F el This is the contribution of hot electrons to the Helmholtz energy. F vib (V,T) is calculated from phonon DOS (p-DOS) as follows:

[0121]

[0122] Where K B Where ω is the Boltzmann constant, and g(ω,V) is the phonon density of states, a function of the phonon frequency ω. It is the simplified Planck constant.

[0123] The contribution of hot electron excitation, Fel(V,T), was obtained through MermIn statistical calculation:

[0124] F el (V,T)=E el (V,T)-TS el (V,T) (4)

[0125] Electron entropy S el Calculated using the following formula:

[0126] S el (V,T)=-k B ∫ n (ε,V){f(ε,V,T)ln f(ε,V,T)+[1-f(ε,V,T)]ln[1-f(ε,V,T)]}d (5)

[0127] Thermoelectron Energy E el (V,T) is calculated by the following formula:

[0128]

[0129] Where n(ε,V) is the density of states (e-DOS) of a single electron with energy ε, f is the Fermi function, and ε F It is Fermi energy.

[0130] Then, the modified Birch-Murnaghan equation of state (EOS) is used to fit the Helmholtz energies at a given temperature for seven given volumes. As shown in Equation (7):

[0131] F(V,T)=a+bV -2 / 3 +cV -4 / 3 +dV -2 +eV -8 / 3 (7)

[0132] Where a, b, c, d, and e are fitting parameters. The equilibrium volume Veq(T) and the minimum Helmholtz free energy F(V) at a given temperature T are given. eq T) is obtained by fitting the following formula:

[0133]

[0134] The equilibrium volume Veq(T) and the coefficient of volumetric thermal expansion (β(T)) are calculated using the following formula:

[0135]

[0136] The relationship between the average linear expansion coefficients α(T) and β(T) is α(T) = β(T) / 3.

[0137] Thermal modulus B T (V,T) is calculated by the following formula:

[0138]

[0139] For the main input data in thermodynamic modeling, the entropy derivation is as follows:

[0140]

[0141] Temperature-dependent enthalpy (H(V) at zero external pressure) eq T) can be calculated using the following formula:

[0142] H(V eq ,T)=U(V eq ,T)=F(V eq ,T)+TS(V eq ,T) (12)

[0143] Where U(Veq,T) is the internal energy, and is equal to the isochoric thermal energy (C0). V (V eq The following relationship exists between T and T:

[0144]

[0145] Isobaric heat capacity is obtained by the following method:

[0146] C P (V eq ,T)=C V (V eq ,T)+V eq TB T (V eq ,T)(β(T)) 2 (14)

[0147] Step 5: Based on the thermal properties of the In-Sn binary crystal structure, In-Ag binary crystal structure, and Sn-Ag binary crystal structure calculated above, and in conjunction with the CALPHAD model, establish a thermodynamic model for Ag-In-Sn. The CALPHAD model is as follows:

[0148] The Gibbs energy of the compound at different temperatures is shown in Equation (15):

[0149]

[0150] Where a, b, c, d, e, and f are model parameters, evaluated from the thermal performance data calculated using the first-principles quasi-harmonic approximation method described above. H SER The enthalpy of the most stable element at 298.15 K and 1 bar is used as the reference state. The Gibbs energy expression for the liquid phase is shown in equation (16):

[0151]

[0152] Where y i It is the mole fraction of component i in the liquid phase. xs G L It is an excess of Gibbs energy. Gibbs energy representing pure liquid phase, excess Gibbs energy xs G L The form is:

[0153]

[0154] in The interaction parameter of order vth between components i and j is obtained from the following equation:

[0155]

[0156] Model parameters v,Liq A and v,Liq B was obtained by evaluating the experimental thermal performance data and liquid-phase related phase boundary data.

[0157] Thermodynamic optimization calculations were performed on the phase diagram of the Ag-In-Sn system using the CALPHAD method. The optimized thermodynamic parameters and thermodynamic model are shown in Table 5, where the thermodynamic model is as follows: Using a trial-and-error method for assignment, and based on thermodynamic optimization calculations, until the phase diagram and thermodynamic data of the Ag-In-Sn system are basically consistent, the liquid phase projection surface of the Ag-In-Sn system is obtained, as shown in the attached figure. Figure 7 As shown. The existence of a eutectic point and its temperature range in the Ag-In-Sn system are determined based on the liquid phase projection surface of the Ag-In-Sn system. The calculation principle of the liquid phase projection surface is as follows: by calculating the relationship between the binary zero-variable reaction and temperature changes with the addition of the third component and changes in composition, a ternary liquid phase projection diagram is obtained. The composition and proportion of the eutectic point are calculated using the thermodynamic lever principle.

[0158] Table 5

[0159]

[0160] Step 6: Based on the obtained liquid phase projection surface of the Ag-In-Sn system, the existence of a eutectic point is analyzed. The composition ratio and temperature of the eutectic point are analyzed as follows: Ag:In:Sn=(12.93-16.68):(38.05-43.24):(40.02-45.85) and 110.30-115.24℃, respectively. That is, the composition ratio of Ag, In and Sn of the selected ternary alloy indium-containing alloy welding material is: (12.93-16.68):(38.05-43.24):(40.02-45.85).

[0161] Step 7: Optimize the ternary crystal structure of the selected ternary alloys Ag, In and Sn, calculate the mechanical properties using the stress-strain method, further calculate the hardness, and calculate the conductivity using the formula for DC conductivity of metals.

[0162] Step 7.1: Calculate the hardness of the ternary alloy Ag, In, and Sn using formula (19). The formula for hardness is as follows:

[0163] H V =0.92K -1.137 G 0.708 (19)

[0164] Here, k is a ratio, k = B / G, where B and G represent the bulk modulus and shear modulus, respectively, and the hardness of Ag-In-Sn is obtained as 12.35HBW.

[0165] Step 7.2: Obtain the conductivity of the ternary alloys Ag, In, and Sn using the formula for DC conductivity of metals, as follows:

[0166]

[0167] Where n is the total charge density of conduction electrons. τ is the effective mass of a free electron. f Let n be the relaxation time. Where n is derived from the following formula:

[0168]

[0169] Where N is the number of conductive charges, calculated using the following formula:

[0170]

[0171] The formula for calculating the effective mass of a free electron is:

[0172]

[0173] The conductivity of the ternary alloy Ag, In, and Sn was found to be 5.54 MS / m, and the conductivity as a function of Ag composition was shown in the attached figure. Figure 12 and attached Figure 14 As shown.

[0174] Step 8: Prepare the sample, and then use differential scanning calorimetry, a high-precision Seebeck coefficient and resistivity tester and an HV-1000A microhardness tester to test the eutectic point composition, electrical conductivity and hardness value.

[0175] Step 8.1: Select 15g of silver, indium and tin blocks, each with a purity of 99.99%, and synthesize them according to the mass ratio Ag:In:Sn = 15.93:41.05:43.02. After weighing and preparing them on an electronic balance, melt and cast them in an intermediate frequency furnace.

[0176] Step 8.2: After metallographic treatment of the surface of the inlaid sample, hardness testing was performed using an HV-1000A microhardness tester. The test force was set to 10 gF, and the loading time was 15 s. Approximately 15 different locations on the same sample were tested, and the average value was taken. The experimental value was 12.70 HBW, which is relatively low, but the error compared to the calculated value (12.35 HBW) is small.

[0177] Step 8.3: The conductivity of the Ag-In-Sn solder was tested using a ZEM-3 Seebeck / resistance testing system manufactured by Advance-Riko, Japan. The experimental conductivity value was 5.45 MS / m, which has a small error compared with the calculated value (5.54 MS / m).

[0178] Step 8.4: The DSC curve of the Ag-In-Sn solder was determined using a NETZSCH DSC 3500 synchronous thermal analyzer. The sample weight was 6 mg, the experimental temperature range was 50℃-250℃, and the heating rate was 10℃ / min. The heating process was carried out under nitrogen protection. The experimental results showed that the eutectic point temperature of the ternary alloy Ag, In, and Sn was 113.30℃, which had a small error compared with the calculated value (110.30-115.24)℃.

[0179] Example 2

[0180] The method for selecting indium-containing alloy welding materials in this embodiment is basically the same as that in Embodiment 1, as detailed below:

[0181] In this embodiment, the method for screening indium-containing alloy welding materials includes the following steps:

[0182] Step 1: Based on currently available databases and relevant literature reports, obtain the elemental and binary crystal structures existing in the Sn-In-Zn system, including elemental Sn, elemental In, and elemental Zn, and the binary crystal structures include In-Sn binary crystal structure, In-Zn binary crystal structure, and Sn-Zn binary crystal structure.

[0183] Sn-In-Zn system: refers to a crystal structure containing three elements: Sn, In and Zn. In-Sn binary crystal structure refers to a binary crystal structure containing two elements: In and Sn. In-Zn binary crystal structure refers to a binary crystal structure containing two elements: In and Zn. Sn-Zn binary crystal structure refers to a binary crystal structure containing two elements: Sn and Zn.

[0184] The data paths open in this embodiment include: Materials Project, OQMD, SprInger Materials, ICSD, and NIST.

[0185] Step 2: Optimize the structures of Sn, In, and Zn elements, specifically the In-Sn binary crystal structure, the In-Zn binary crystal structure, and the Sn-Zn binary crystal structure, and calculate the formation enthalpy of Sn, In, and Zn elements, specifically the In-Sn binary crystal structure, the In-Zn binary crystal structure, and the Sn-Zn binary crystal structure.

[0186] Step 2.1: First, set the parameters "ISIF=3, IBRION=2" to perform low-precision structure optimization on Sn, In, and Zn elements, as well as the In-Sn, In-Zn, and Sn-Zn binary crystal structures. The energy convergence criterion is 10. -6 eV, the convergence criterion for force is

[0187] Step 2.2: After the low-precision optimization is completed, high-precision structural optimization is performed again on the low-precision optimized Sn, In, and Zn elements, as well as the In-Sn binary crystal structure, the In-Zn binary crystal structure, and the Sn-Zn binary crystal structure. The energy convergence criterion is 10. -8 eV, the convergence criterion for force is The convergence criteria were not met after two optimizations. The optimization parameters were modified to "ISIF=2,IBRION=1", and low-precision and high-precision structural optimizations were performed again on Sn, In, and Zn elements, as well as the In-Sn, In-Zn, and Sn-Zn binary crystal structures, which finally met the convergence criteria.

[0188] Step 2.3: Calculate the formation enthalpy of Sn, In, and Zn elements, as well as the In-Sn binary crystal structure, In-Zn binary crystal structure, and Sn-Zn binary crystal structure, using the formation enthalpy calculation formula. Taking the In-Zn binary crystal structure as an example, the formation enthalpy calculation formula is shown in formula (1):

[0189]

[0190] In the formula: ΔH represents the enthalpy of formation, E total E represents the total energy of the In-Zn binary crystal structure. In and E Zn represents the energy of elemental In and Zn, respectively. x and y represent the number of atoms of elemental In and Zn in the In-Zn binary crystal structure, respectively.

[0191] Step 3: Based on the highly optimized Sn, In, and Zn elements, construct energy convex hull diagrams for the formation enthalpies of the In-Sn, In-Zn, and Sn-Zn binary crystal structures, and analyze their thermodynamic stability. Details are as follows:

[0192] Step 3.1: Construct energy convex hull diagrams for the In-Sn binary crystal structure, the In-Zn binary crystal structure, and the Sn-Zn binary crystal structure, respectively, with the enthalpy of formation as the ordinate and the atomic fraction as the abscissa. (See attached diagram.) Figure 4 As shown.

[0193] Step 3.2: After constructing the energy convex hull diagrams of the In-Sn binary crystal structure, the In-Zn binary crystal structure, and the Sn-Zn binary crystal structure, determine whether each binary crystal structure is thermodynamically stable based on whether the formation enthalpy of the In-Sn binary crystal structure, the In-Zn binary crystal structure, and the Sn-Zn binary crystal structure is less than 0.0 eV.

[0194] If the formation enthalpy of the binary crystal structure is greater than 0.0 eV, it indicates that the binary crystal structure is thermodynamically unstable. If the formation enthalpy of the binary crystal structure is less than 0.0 eV, but the formation enthalpy of the binary crystal structure does not conform to the rules of the constructed convex hull diagram, it indicates that the crystal structure is not the most stable structure in the system. If the formation enthalpy of the binary crystal structure conforms to the rules of the constructed convex hull diagram, it indicates that the crystal structure is the most stable structure in the system. Figure 4 As shown, the formation enthalpy of all compounds in the Sn-In-Zn system is greater than 0.0 eV, indicating that all compounds in the Sn-In-Zn system are thermodynamically unstable.

[0195] Step 4: Based on the first-principles quasi-harmonic approximation method, i.e., the QHA method, the thermal properties of the highly optimized In-Sn binary crystal structure, In-Zn binary crystal structure, and Sn-Zn binary crystal structure are calculated respectively.

[0196] Step 4.1: Phonon spectrum calculations are performed on each of the highly optimized In-Sn binary crystal structure, In-Zn binary crystal structure, and Sn-Zn binary crystal structure using Phonopy software to select In-Sn binary crystal structure, In-Zn binary crystal structure, and Sn-Zn binary crystal structure with no imaginary frequency in the phonon spectrum.

[0197] Specifically, this involves further optimizing the already highly precise structure, raising the force convergence criterion to a higher level. The energy convergence criterion remains unchanged. The In-Sn binary crystal structure, the In-Zn binary crystal structure, and the Sn-Zn binary crystal structure are expanded to 2*2*2, respectively. The corresponding high-symmetry k-points are halved, and phonon spectrum calculations are attempted again until the phonon spectrum has no imaginary frequencies.

[0198] Step 4.3: Perform variable volume energy and volume calculations on the selected In-Sn binary crystal structures, In-Zn binary crystal structures, and Sn-Zn binary crystal structures with no imaginary frequency in their phonon spectra.

[0199] Specifically, the phonon spectra of In-Sn binary crystal structures, In-Zn binary crystal structures, and Sn-Zn binary crystal structures in volumes of 0.97, 0.98, 0.99, 1.00, 1.01, 1.02, and 1.03 were calculated one by one. The corresponding thermal properties were obtained based on the quasi-static approximation method. The thermal properties described in this embodiment are Helmholtz energies.

[0200] The Helmholtz energy is decomposed into three cumulative contributions, as shown in Equation (2):

[0201] F(V,T)=E c (V)+F vib (V,T)+F el (V,T) (2)

[0202] In the formula, F(V,T) represents the Helmholtz energy as a function of temperature T and volume V; E c In the quasi-static approximation method, the directly output 0K static total energy; F vib For vibrational free energy; F el This is the contribution of hot electrons to the Helmholtz energy. F vib (V,T) is calculated from phonon DOS (p-DOS) as follows:

[0203]

[0204] Where K B Where ω is the Boltzmann constant, and g(ω,V) is the phonon density of states, a function of the phonon frequency ω. It is the simplified Planck constant.

[0205] The contribution of hot electron excitation, Fel(V,T), was obtained through MermIn statistical calculation:

[0206] F el (V,T)=E el (V,T)-TS el (V,T) (4)

[0207] Electron entropy S el Calculated using the following formula:

[0208] S el (V,T)=-k B ∫n(ε,V){f(ε,V,T)ln f(ε,V,T)+[1-f(ε,V,T)]ln[1-f(ε,V,T)]}d (5)

[0209] Thermoelectron Energy E el (V,T) is calculated by the following formula:

[0210]

[0211] Where n(ε,V) is the density of states (e-DOS) of a single electron with energy ε, f is the Fermi function, and ε F It is Fermi energy.

[0212] Then, the modified Birch-Murn-Znhan equation of state (EOS) is used to fit the Helmholtz energies at a given temperature for seven given volumes, as shown in Equation (7):

[0213] F(V,T)=a+bV -2 / 3 +cV -4 / 3 +dV -2 +eV -8 / 3 (7)

[0214] Where a, b, c, d, and e are fitting parameters. The equilibrium volume Veq(T) and the minimum Helmholtz free energy (F(V)) at a given temperature T are given. eq T) is obtained by fitting the following formula:

[0215]

[0216] The equilibrium volume Veq(T) and the coefficient of volumetric thermal expansion (β(T)) are calculated using the following formula:

[0217]

[0218] The relationship between the average linear expansion coefficients α(T) and β(T) is α(T) = β(T) / 3.

[0219] Thermal modulus B T (V,T) is calculated by the following formula:

[0220]

[0221] For the main input data in thermodynamic modeling, the entropy derivation is as follows:

[0222]

[0223] Temperature-dependent enthalpy (H(V) at zero external pressure) eq T) can be calculated using the following formula:

[0224] H(V eq ,T)=U(V eq ,T)=F(V eq ,T)+TS(V eq ,T) (12)

[0225] Where U(Veq,T) is the internal energy, and is equal to the isochoric thermal energy (C0). V (V eq The following relationship exists between T and T:

[0226]

[0227] Isobaric heat capacity is obtained by the following method:

[0228] C P (V eq ,T)=C V (V eq ,T)+V eq TB T (V eq ,T)(β(T)) 2 (14)

[0229] Step 5: The thermal properties of the In-Sn binary crystal structure, the In-Zn binary crystal structure, and the Sn-Zn binary crystal structure are analyzed. A thermodynamic model of the Sn-In-Zn ternary alloy is then established using the CALPHAD model. The CALPHAD model is as follows:

[0230] The Gibbs energy of the compound at different temperatures is shown in Equation (15):

[0231]

[0232] Where a, b, c, d, e, and f are model parameters, evaluated from the thermal performance data calculated using the first-principles quasi-harmonic approximation method described above. H SER The enthalpy of the most stable element at 298.15 K and 1 bar is used as the reference state. The Gibbs energy expression for the liquid phase is shown in equation (16):

[0233]

[0234] Where y i It is the mole fraction of component i in the liquid phase. xs G L It is an excess of Gibbs energy. Gibbs energy representing pure liquid phase, excess Gibbs energy xs GL The form is:

[0235]

[0236] in The interaction parameter of order vth between components i and j is obtained from the following equation:

[0237]

[0238] Model parameters v,Liq A and v,Liq B was obtained by evaluating experimental thermochemical data and liquid-phase-related phase boundary data.

[0239] The phase diagram of the Sn-In-Zn system was thermodynamically optimized and calculated using the CALPHAD method. The optimized thermodynamic parameters and thermodynamic model are shown in Table 6. The thermodynamic model is as follows:

[0240] Using a trial-and-error method, values ​​were assigned, and thermodynamic optimization calculations were performed until the phase diagram and thermodynamic data of the Sn-In-Zn system were essentially consistent. The liquid phase projection surface of the Sn-In-Zn system was obtained, as shown in the attached figure. Figure 8 As shown. The existence of a eutectic point and its temperature range in the Sn-In-Zn system are determined based on the liquid phase projection surface of the Sn-In-Zn system.

[0241] Table 6

[0242]

[0243]

[0244] Step 6: Based on the obtained liquid phase projection surface of the Sn-In-Zn system, the existence of a eutectic point is analyzed. The composition ratio and temperature of the eutectic point are: In:Sn:Zn = (34.47-38.86):(45.02-49.56):(14.36-18.12) and (104.80-108.34)℃, respectively. That is, the composition ratio of In, Sn and Zn in the selected ternary alloy indium-containing alloy welding material is: (34.47-38.86):(45.02-49.56):(14.36-18.12).

[0245] Step 7: The structure of the ternary indium-containing alloy welded material (In, Sn, and Zn) selected in Step 6 is optimized. The mechanical properties of the material are calculated using the stress-strain method, and the hardness is further calculated. The electrical conductivity is calculated using the formula for DC electrical conductivity of metals. The hardness of the ternary indium-containing alloy welded material (In, Sn, and Zn) is 6.39 HBW, and the electrical conductivity of the Sn-In-Zn system is 6.69 MS / m. The variation of its conductivity with Zn composition is shown in the attached figure. Figure 13 and attached Figure 15 As shown.

[0246] Step 8: Prepare the sample, and then use differential scanning calorimetry, a high-precision Seebeck coefficient and resistivity tester and an HV-1000A microhardness tester to test its eutectic point composition, electrical conductivity and hardness value.

[0247] Step 8.1: Select 15g of zinc, indium and tin blocks, each with a purity of 99.99%, and synthesize them according to the mass ratio In:Sn:Zn = 36.86:47.02:16.12. After weighing and preparing them on an electronic balance, melt and cast them in an intermediate frequency furnace.

[0248] Step 8.2: After metallographic treatment of the surface of the inlaid sample, hardness testing was performed using an HV-1000A microhardness tester. The test force was set to 10 gF, and the loading time was 15 s. Approximately 15 different locations on the same sample were measured, and the average value was taken. The experimental value was 6.30 HBW, which is relatively low, but the error is small compared to the calculated value of 6.39 HBW.

[0249] Step 8.3: The conductivity of the Sn-In-Zn solder was tested using a ZEM-3 Seebeck / resistance testing system manufactured by Advance-Riko, Japan. The experimental conductivity value was 6.71 MS / m, which has a small error compared to the calculated value of 6.69 MS / m.

[0250] Step 8.4: The DSC curve of the Sn-In-Zn solder was determined using a NETZSCH DSC 3500 synchronous thermal analyzer. The sample weight was 6 mg, the experimental temperature range was 50℃-250℃, and the heating rate was 10℃ / min. The heating process was carried out under nitrogen protection. The experimental results showed that the eutectic point temperature of Zn-In-Zn was 106.80℃, which had a small error compared with the calculated value of (104.80-108.34)℃.

[0251] The methods described in Examples 1 and 2 for screening indium-containing alloy welding materials can overcome the shortcomings of the traditional "trial and error method," save resources and time, and establish a thermodynamic model of the ternary alloy system based on high-throughput first-principles calculations combined with the CALPHAD model to screen out ternary alloys with low eutectic point composition. Moreover, experimental verification shows that the error range is very small.

[0252] The embodiments of the method of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made according to the purpose of the invention. Any parameter changes or calculation simplifications made based on the principle of the technical solution of the present invention, as long as they meet the purpose of the invention and do not deviate from the principle and concept of the present invention of a method for screening indium alloy welding materials and indium alloy welding materials, shall fall within the protection scope of the present invention.

Claims

1. A method for screening indium-containing alloy welding materials, characterized in that, Includes the following steps: Step 1: Obtain the elemental and binary crystal structures present in the TM1-In-TM2 system, where TM1 represents one of Sn and Ag, and TM2 represents one of Sb, Ag, Zn, and Cu. Step 2: Optimize the structure of the elemental and binary crystal structures obtained in Step 1, and calculate the formation enthalpy of each elemental and binary crystal structure based on the optimized structure. Step 3: Construct an energy convex hull diagram based on the formation enthalpy of each element and each binary crystal structure calculated in Step 2. Analyze the thermodynamic stability of each element and each binary crystal structure based on the constructed energy convex hull diagram. Step 4: Based on the quasi-harmonic approximation method, calculate the thermal properties of each binary crystal structure after structural optimization. Step 5: Based on the thermal properties of each binary crystal structure calculated in Step 4, and combined with the CALPHAD model, establish a thermodynamic model of the TM1-In-TM2 system, and then obtain the liquid phase projection surface of the TM1-In-TM2 system. Step 6: Based on the obtained liquid phase projection surface of the TM1-In-TM2 system, analyze the composition ratio and temperature of the eutectic point, and screen out the corresponding low-melting-point eutectic indium-containing alloy welding materials. Step 4 includes: Step 4.1: Perform phonon spectrum calculations on each of the high-precision optimized binary crystal structures and select binary crystal structures with no imaginary frequencies in their phonon spectra. Step 4.2: For each binary crystal structure with no imaginary frequency in the selected phonon spectrum, perform variable volume energy and volume calculations. Specifically, calculate the phonon spectrum of each binary crystal structure with volumes of 0.97, 0.98, 0.99, 1.00, 1.01, 1.02, and 1.03, and obtain the corresponding thermal properties based on the quasi-static approximation method. Step 4.2 includes: calculating the Helmholtz energy of the thermal properties, and the specific calculation method is as follows: The Helmholtz energy is decomposed into three cumulative contributions, as shown in Equation (2): where F(V, T) represents the Helmholtz energy as a function of temperature T and volume V; E c is the directly output 0 K static total energy in the quasi-static approximation method; F vib is the vibrational free energy; F el is the contribution of hot electrons to the Helmholtz energy; F vib (V, T) is calculated from the phonon DOS (p-DOS) as: Where K B It is Boltzmann's constant. The phonon density of states is a function of the phonon frequency ω. It is the simplified Planck constant; The contribution F of hot electron excitation el (V, T) is obtained through MermIn statistical calculations: Electron entropy S el Calculated using the following formula: Thermoelectron Energy E el (V,T) is calculated by the following formula: in The density of electronic states is a function of the energy ε of a single electron, where f is the Fermi function and ε is the electron density of states. F It is Fermi energy; Step 4.2 further includes: fitting the Helmholtz energy at a given temperature for seven given volumes using the Birch-Murnaghan equation of state; as shown in Equation (7): Where a, b, c, d, and e are fitting parameters; the equilibrium volume Viq(T) and the minimum Helmholtz free energy at a given temperature T are... The following formula is used for fitting: Calculated equilibrium volume V eq (T), the coefficient of volumetric thermal expansion (#imgpt11#) is calculated by the following formula: The relationship between the average linear expansion coefficients #imgpt13# and #imgpt14# is #imgpt15# = #imgpt16# / 3; Thermal modulus B T (V,T) is calculated by the following formula: For the input data in thermodynamic modeling, the entropy derivation is: The temperature-dependent enthalpy at zero external pressure (#imgpt19#) is calculated by the following formula: Where U(V) eq T) is the internal energy, and it has the following relationship with isochoric thermal melting (#imgpt21#): The isobaric heat capacity is obtained from formula (14):

2. The method for screening indium-containing alloy welding materials according to claim 1, characterized in that: Step 3 includes: Step 3.1: Construct energy convex hull diagrams for each binary crystal structure with the enthalpy of formation as the ordinate and the atomic fraction as the abscissa. Step 3.2: After constructing the energy convex hull diagrams of each binary crystal structure, the thermodynamic stability of each binary crystal structure is determined based on whether the formation enthalpy of each binary crystal structure is less than 0.0 eV.

3. The method for screening indium-containing alloy welding materials according to claim 2, characterized in that, In step 3.2, if the formation enthalpy of the binary crystal structure is greater than 0.0 eV, then the binary crystal structure is thermodynamically unstable; if the formation enthalpy of the binary crystal structure is less than 0.0 eV, but the formation enthalpy of the binary crystal structure does not conform to the rules of the constructed energy convex hull diagram, then the binary crystal structure is not the most stable structure in the TM1-In-TM2 system; if the formation enthalpy of the binary crystal structure is less than 0.0 eV, and the formation enthalpy of the binary crystal structure conforms to the rules of the constructed energy convex hull diagram, then the binary crystal structure is the most stable structure in the TM1-In-TM2 system.

4. An indium-containing alloy welding material, characterized in that, The indium-containing alloy welding materials were selected by any one of the methods described in claims 1-3.

5. The indium-containing alloy welding material according to claim 4, characterized in that, This includes indium-containing alloy welding materials with a Sn:In:Ag ratio of (40.02-45.85):(38.05-43.24):(12.93-16.68), Sn:In:Zn ratio of (45.02-49.56):(34.47-38.86):(14.36-18.12), Sn:In:Cu ratio of (46.78-50.92):(44.56-48.32):(3.68-6.76), and Ag:In:Cu ratio of (7.20-11.40):(80.44-84.56). Indium-containing alloy welding materials with an Ag:In:Sb ratio of (6.36-9.66) and (76.56-80.34):(11.64-14.78) are used.

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