A method for screening a bismuth-containing alloy welding material and a bismuth-containing alloy welding material

Abstract

The present invention relates to the technical field of welding material screening, and specifically to a method for screening bismuth-containing alloy welding materials. The method comprises using first principles to perform low-precision to high-precision structural optimization of each binary crystal structure in a Sn-Bi-TM system, calculating the basic phase information of each binary crystal structure using Vasp; calculating the phonon spectrum of each binary crystal structure based on the high-precision optimized binary crystal structures; calculating the thermal properties of each binary crystal structure using a quasi-harmonic approximation method to obtain thermodynamic data, evaluating CALPHAD model parameters based on the thermodynamic data, and establishing a thermodynamic model of the Sn-Bi-TM system; and obtaining the liquid phase projection surface of each binary crystal structure based on the thermodynamic model, finding the eutectic point and temperature, and screening the bismuth-containing alloy welding material. The present invention also discloses two bismuth-containing alloy welding materials. The composition ratios of these two low-melting-point eutectic bismuth-containing alloy welding materials are discovered for the first time, and they have the advantages of low melting point, high powder quality, and no sticking.

Description

Technical Field

[0001] The present invention relates to the technical field of screening welding materials, and in particular to a method for screening bismuth-containing alloy welding materials and the bismuth-containing alloy welding materials. Background Art

[0002] For circuits formed through packaging and assembly, the performance of solder alloys plays a crucial role in the overall operation of the circuit. In microelectronic interconnection, research on solder alloy materials focuses on low melting points, excellent flowability and wettability, sufficient conductivity, corrosion resistance, and mechanical strength. For temperature-sensitive materials, such as electronic components with poor heat resistance and temperature sensors, soldering must be performed at low temperatures, where traditional solder alloys exhibit limitations. Sn-Bi-based solders offer excellent processing conditions, solder cost, mechanical properties, and reliability, making them the most widely used low-temperature lead-free solders. However, Sn-Bi-based solders exhibit aging issues during processing, such as brittleness, low ductility, and Bi segregation, which require improvement. Research has shown that the addition of trace alloying elements such as Ag, Cu, and Zn can refine the microstructure and improve the mechanical properties of Sn-Bi-based lead-free solders. Adding a certain amount of Bi can also lower the melting point and improve wettability. Therefore, there is an urgent need to find new low-melting-point eutectic bismuth-containing welding materials to solve the above problems. However, the research and development of new solder welding materials is an expensive and time-consuming task, so a new method is needed to improve R&D efficiency and reduce R&D costs. Summary of the Invention

[0003] The present invention provides a method for screening bismuth-containing alloy welding materials, comprising the following steps:

[0004] Step 1, obtaining the binary crystal structure existing in the Sn-Bi-TM system, where TM represents one of Sb, Ag, Zn, and Cu;

[0005] Step 2: Using the first principles based on density functional theory to perform low-precision to high-precision structural optimization on each binary crystal structure, and calculate the basic phase information of each binary crystal structure;

[0006] Step 3, based on each binary crystal structure after high-precision optimization, calculating the phonon spectrum of each binary crystal structure;

[0007] Step 4, calculating the thermal properties of each binary crystal structure based on the quasi-harmonic approximation method to obtain thermodynamic data;

[0008] Step 5, using the thermodynamic data obtained in step 4 to evaluate the CALPHAD model parameters and establish a thermodynamic model for the Sn-Bi-TM system;

[0009] Step 6: Based on the thermodynamic model, the liquid phase projection surface of each binary crystal structure is obtained, and the eutectic point and temperature are found based on the liquid phase projection surface to screen out the bismuth-containing alloy welding material.

[0010] A preferred embodiment of the present invention is that step 3 includes: setting parameters "ISIF=2, IBRION=8", using the Phonopy finite displacement method to calculate the phonon spectrum of each binary crystal structure one by one, and screening out binary crystal structures with no imaginary frequency in the phonon spectrum.

[0011] A preferred embodiment of the present invention is that, in step 5, the CALPHAD model is as follows:

[0012] The Gibbs energy of a compound at different temperatures is shown below:

[0013]

[0014] where a, b, c, d, e and f are model parameters evaluated from thermodynamic data calculated by first-principles quasi-harmonic methods, H SER The enthalpy of the most stable element at 298.15K and 1 bar is used as the reference state.

[0015] A preferred embodiment of the present invention is that step 5 further comprises:

[0016] The Gibbs energy expression of the liquid phase is:

[0017]

[0018] where y i is the mole fraction of component i in the liquid phase, xs G L is the excess Gibbs energy phase, Represents the Gibbs energy of the pure liquid phase, excess Gibbs energy xs G L The form is:

[0019]

[0020] in is the vth-order interaction parameter between components i and j, which is given by:

[0021]

[0022] Model parameters v,Liq A and v,Liq B is estimated from experimental thermodynamic data and liquid-related phase boundary data.

[0023] A preferred embodiment of the present invention is that, in step 5, the thermodynamic model of the Sn-Bi-Zn system is:

[0024]

[0025] The thermodynamic model of the Sn-Bi-Ag system is:

[0026]

[0027] A preferred embodiment of the present invention further includes step 7, wherein the structure of the selected bismuth-containing alloy welding material is optimized, and mechanical properties are calculated using a stress-strain method, including hardness calculation, and electrical conductivity calculation using a metal DC conductivity formula.

[0028] The method presented in this paper overcomes the shortcomings of traditional trial-and-error methods, conserving resources and time. Based on high-throughput first-principles calculations combined with the CALPHAD model, a thermodynamic model of the Sn-Bi-TM system is established. This method identifies ternary alloys with low-melting-point eutectic compositions, and experimentally validates the results with a very narrow error margin. This improves the efficiency and reduces the cost of developing new bismuth-containing ternary alloy welding materials.

[0029] The present invention also discloses a bismuth-containing alloy welding material, which is obtained by screening using any of the aforementioned methods for screening bismuth-containing alloy welding materials.

[0030] Furthermore, the bismuth-containing alloy welding material of the present invention includes a bismuth-containing alloy welding material having a composition ratio of Sn:Bi:Ag of (32.51-38.54):(44.70-52.68):(13.79-16.88), and a bismuth-containing alloy welding material having a composition ratio of Sn:Bi:Zn of (20.76-34.09):(49.54-55.31):(10.64-14.06).

[0031] Furthermore, the eutectic temperature of the bismuth-containing alloy welding material with a screened Sn:Bi:Zn composition ratio of (20.76-34.09):(49.54-55.31):(10.64-14.06) is 128.68-135.76°C; the eutectic temperature of the bismuth-containing alloy welding material with a screened Sn:Bi:Ag composition ratio of (32.51-38.54):(44.70-52.68):(13.79-16.88) is 132.87-140.65°C.

[0032] Compared with other alloy welding materials, the advantages of the selected Sn-Bi-Zn and Sn-Bi-Ag low melting point bismuth-containing eutectic welding materials are as follows:

[0033] (1) The compositions of Sn-Bi-Zn and Sn-Bi-Ag low-melting-point bismuth-containing eutectic welding materials are discovered for the first time.

[0034] (2) The melting points of Sn-Bi-Zn and Sn-Bi-Ag low-melting-point bismuth-containing eutectic welding materials are very low, ranging from 106.04℃ to 143.85℃;

[0035] Sn-Bi-Zn and Sn-Bi-Ag low melting point bismuth-containing eutectic welding materials are eutectic alloys with no solid-liquid two-phase region, no adhesion phenomenon, easy processing and high powder quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Attachment Figure 1 A flow chart of the method for screening bismuth-containing alloy welding materials according to the present invention;

[0037] Attachment Figure 2 It is the liquid phase projection surface of Sn-Bi-Zn system;

[0038] Attachment Figure 3 It is the liquid phase projection surface of the Sn-Bi-Ag system. DETAILED DESCRIPTION

[0039] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0040] This study, based on publicly available databases and relevant literature, identified 78 crystal structures in the Sn-Bi-TM system, including 40 binary structures. TM represents one of Sb, Ag, Zn, and Cu. The publicly available databases include the Materials Project, OQMD, Springer Materials, ICSD, and NIST. The Sn-Bi-TM system refers to crystal structures containing one or two of the three elements Sn, Bi, and TM.

[0041] (1) Using the first principles method based on density functional theory, 78 crystal structures were optimized from low precision to high precision. The basic phase information of each crystal structure was calculated by Vasp. The basic phase information of 78 crystal structures in the Sn-Bi-TM system was obtained, including lattice constants, space groups, volumes, densities, and formation enthalpies. The calculation results are shown in Table 1. In Table 1, a, b, c, α, β, and γ represent lattice constants, and ΔH represents formation enthalpy.

[0042] Table 1

[0043]

[0044]

[0045]

[0046] (2) Based on the 40 binary crystal structures after high-precision optimization, the phonon spectra of these 40 binary crystal structures were calculated using Phonopy software.

[0047] (3) Based on the quasi-harmonic approximation method, namely the QHA method, the thermal properties of each binary crystal structure are calculated to obtain thermodynamic data.

[0048] (4) The CALPHAD model parameters were evaluated based on the thermodynamic data obtained by the quasi-harmonic approximation method. Finally, a thermodynamic model of the Sn-Bi-TM system was established. The liquid phase projection surface of each binary crystal structure was obtained based on the thermodynamic model. The eutectic point and temperature were found based on the liquid phase projection surface, and bismuth-containing alloy welding materials were screened out.

[0049] Compared with other alloy welding materials, the advantages of the screened and experimentally verified Sn-Bi-Zn and Sn-Bi-Ag low melting point bismuth-containing eutectic welding materials are as follows:

[0050] (1) The compositions of Sn-Bi-Zn and Sn-Bi-Ag low-melting-point bismuth-containing eutectic welding materials are discovered for the first time.

[0051] (2) The melting points of Sn-Bi-Zn and Sn-Bi-Ag low-melting-point bismuth-containing eutectic welding materials are very low, ranging from 106.04℃ to 143.85℃. The composition and melting point are shown in Table 2.

[0052] Table 2

[0053] Serial number system Ingredients / wt% Calculated value / ℃ Experimental value / ℃ 1 Bi-Sn-Zn Bi:Sn:Zn=53.31:34.09:12.60 131.68 133.50 2 Ag-Bi-Sn Ag:Bi:Sn=13.79:49.70:36.51 136.87 137.70

[0054] (3) The calculated values of hardness and conductivity of Sn-Bi-Zn and Sn-Bi-Ag are consistent with the experimental values, as shown in Tables 3 and 4.

[0055] Table 3

[0056] serial number Alloy name Calculated value Experimental value-MS / m 1 Bi-Sn-Zn 2.89 2.99 2 Ag-Bi-Sn 2.50 2.44

[0057] Table 4

[0058] serial number Alloy name Calculated value Experimental value-HBW 1 Bi-Sn-Zn 14.01 14.10 2 Ag-Bi-Sn 28.58 28.60

[0059] (4) The Sn-Bi-Zn and Sn-Bi-Ag low-melting-point bismuth-containing eutectic welding materials are eutectic alloys with no solid-liquid two-phase region, no adhesion phenomenon, easy processing, and high powder quality.

[0060] The following describes in detail the specific steps for selecting bismuth-containing alloy welding materials from the Sn-Bi-Ag and Sn-Bi-Zn systems. The methods for selecting bismuth-containing alloy welding materials from other systems are similar to those for these two systems.

[0061] Example 1

[0062] The method for screening bismuth-containing alloy welding materials in this embodiment comprises the following steps:

[0063] Step 1: Based on currently available databases and relevant literature reports, obtain the binary crystal structures existing in the Sn-Bi-Zn system, including the Sn-Bi binary crystal structure, the Bi-Zn binary crystal structure, and the Sn-Zn binary crystal structure. Among them, the Sn-Bi-Zn system refers to a crystal structure containing one or two of the three elements Sn, Bi, and Zn, the Sn-Bi binary crystal structure refers to a binary crystal structure containing Bi and Sn, the Bi-Zn binary crystal structure refers to a binary crystal structure containing Bi and Zn, and the Sn-Zn binary crystal structure refers to a binary crystal structure containing Sn and Zn.

[0064] Step 2: Using the first-principles calculation method based on density functional theory, the initial Sn-Bi binary crystal structure, Bi-Zn binary crystal structure, and Sn-Zn binary crystal structure are subjected to low-precision structural optimization by Vasp software. Then, high-precision structural optimization is performed on the low-precision optimized Sn-Bi binary crystal structure, Bi-Zn binary crystal structure, and Sn-Zn binary crystal structure respectively. Based on the high-precision optimized Sn-Bi binary crystal structure, Bi-Zn binary crystal structure, and Sn-Zn binary crystal structure, basic phase information is calculated, including formation enthalpy. The calculation results are shown in Table 1. Step 2 specifically includes:

[0065] In step 2.1, selecting appropriate key parameters helps improve the accuracy and efficiency of the calculation. The selection of the cutoff energy and the density of the k-point mesh is crucial. A k-point mesh with a precision of 0.03 was generated using Vaspkit function 102. The cutoff energy was set to 1.5 times the element ENMAX in the POTCAR file.

[0066] Step 2.2: First, set the parameters “ISIF=3, IBRION=2” and perform low-precision structure optimization on the Sn-Bi binary crystal structure, Bi-Zn binary crystal structure, and Sn-Zn binary crystal structure respectively. The energy convergence criterion is 10 -6 eV, the force convergence criterion is Reach the convergence criterion.

[0067] Step 2.3: After the low-precision structure optimization is completed, the high-precision structure optimization is performed again for the Sn-Bi binary crystal structure, Bi-Zn binary crystal structure, and Sn-Zn binary crystal structure after the low-precision structure optimization. The energy convergence criterion is 10 -8 eV, the force convergence criterion is

[0068] In step 2.4, based on the highly-accurately optimized Sn-Bi binary crystal structure, Bi-Zn binary crystal structure, and Sn-Zn binary crystal structure, the formation enthalpy of each binary crystal structure is calculated using the formation enthalpy calculation formula to serve as a parameter for the CALPHAD model. Taking the Sn-Bi binary crystal structure as an example, the formation enthalpy calculation formula is shown in formula (1).

[0069]

[0070] Where ΔH represents the formation enthalpy, E total represents the total energy of the Sn-Bi binary crystal structure, E Bi and E Sn are the energies of elemental Bi and Sn, respectively. x and y are the atomic numbers of elemental Bi and Sn in the Sn-Bi binary crystal structure, respectively.

[0071] Step 3: Based on the high-precision optimized Sn-Bi binary crystal structure, Bi-Zn binary crystal structure, and Sn-Zn binary crystal structure, Phonopy software is used to calculate the phonon spectrum of the Sn-Bi binary crystal structure, Bi-Zn binary crystal structure, and Sn-Zn binary crystal structure, respectively, to screen out binary crystal structures with no imaginary frequency in the phonon spectrum, as follows:

[0072] Taking the Sn-Bi binary crystal structure as an example, based on the highly optimized Sn-Bi binary crystal structure, the Phonopy software was used to expand it, generating a SPOCAR file. Based on the symmetry of the Sn-Bi binary crystal structure, supercells with different displacements were generated. The more complex the symmetry, the greater the number of supercells with different displacements, and the greater the computational effort. With the parameters "ISIF = 2, IBRION = 8," the supercells with different displacements were calculated sequentially.

[0073] Step 4: Based on the first-principles quasi-harmonic approximation method, i.e., the QHA method, the thermal properties of the screened Sn-Bi binary crystal structure, Bi-Zn binary crystal structure, and Sn-Zn binary crystal structure with no imaginary frequency in the phonon spectrum are calculated.

[0074] The specific steps are as follows:

[0075] Based on the Sn-Bi binary crystal structure, Bi-Zn binary crystal structure, and Sn-Zn binary crystal structure with no imaginary frequency in the phonon spectrum, the energy and volume calculation of variable volume is performed. Specifically:

[0076] Phonon spectra of the Sn-Bi binary crystal structure, Bi-Zn binary crystal structure, and Sn-Zn binary crystal structure were calculated at volume levels of 0.97, 0.98, 0.99, 1.00, 1.01, 1.02, and 1.03, and the corresponding thermal properties were obtained using the quasi-harmonic approximation method. The thermal properties refer to the Helmholtz energy.

[0077] The Helmholtz energy is decomposed into three cumulative contributions. As shown in formula (2):

[0078] F(V,T)=E c (V)+F vib (V,T)+F el (V,T) (2)

[0079] Where F(V,T) represents the Helmholtz energy as a function of temperature T and volume V; E c is the static total energy of 0K directly output by the quasi-harmonic approximation method based on the first principle; F vib is the vibrational free energy; F el is the contribution of hot electrons to the Helmholtz energy.

[0080] F vib (V,T) is calculated from the phonon DOS (p-DOS) as shown in formula (3):

[0081]

[0082] Where K B is the Boltzmann constant, g(ω,V) is the phonon state density as a function of the phonon frequency ω, is the simplified Planck constant. The contribution of hot electron excitation F el (V, T) is calculated by MermIn statistics, as shown in formula (4):

[0083] F el (V,T)=E el (V,T)-TS el (V,T) (4)

[0084] Electron entropy S el Calculated by the following formula:

[0085] 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)

[0086] The hot electron energy is calculated by the following formula:

[0087]

[0088] where n(ε,V) is the electron density of states (e-DOS) as a function of the single electron energy ε, f is the Fermi function, and ε F It's Fermi energy.

[0089] The modified Birch-Murnaghan equation of state (EOS) is then used to fit the Helmholtz energy at a given temperature for seven given volumes, as shown in Equation (7):

[0090] F(V,T)=a+bV -2 / 3 +cV -4 / 3 +dV -2 +eV -8 / 3 (6)

[0091] Where a, b, c, d and e are fitting parameters. The equilibrium volume V at a given temperature T eq (T) and minimum Helmholtz free energy (F(V eq ,T)) is obtained by fitting the following formula:

[0092]

[0093] Calculated equilibrium volume V eq (T), the volume thermal expansion coefficient (β(T)) is calculated by the following formula:

[0094]

[0095] The relationship between the average linear expansion coefficients α(T) and β(T) is α(T)=β(T) / 3.

[0096] Adiabatic modulus B T (V,T) is calculated by the following formula:

[0097]

[0098] For the main input data of thermodynamic modeling, entropy is derived as:

[0099]

[0100] Temperature-dependent enthalpy (H(V eq ,T)) is calculated by the following formula:

[0101] H(Veq ,T)=U(V eq ,T)=F(V eq ,T)+TS(V eq ,T) (11)

[0102] Where U(Veq,T) is the internal energy, which is the same as the isochoric melting (C V (V eq ,T)) has the following relationship:

[0103]

[0104] The isobaric heat capacity is obtained from the following formula:

[0105] C P (V eq ,T)=C V (V eq ,T)+V eq TB T (V eq ,T)(β(T)) 2 (13)

[0106] Step 5: Based on the thermal properties of the Sn-Bi binary crystal structure, the Bi-Zn binary crystal structure, and the Sn-Zn binary crystal structure calculated above, and combined with the CALPHAD model, a thermodynamic model of the Sn-Bi-Zn system is established. The CALPHAD model used is as follows:

[0107] The Gibbs energy of a compound at different temperatures is shown below:

[0108]

[0109] Where a, b, c, d, e and f are model parameters, which are evaluated from the thermodynamic data obtained by the first-principles quasi-harmonic method described above. SER The enthalpy of the most stable element at 298.15K and 1 bar is used as the reference state. The Gibbs energy expression of the liquid phase is:

[0110]

[0111] where y i is the mole fraction of component i in the liquid phase, xs G L is the excess Gibbs energy phase, Represents the Gibbs energy of the pure liquid phase, excess Gibbs energy xs G L The form is:

[0112]

[0113] in is the vth-order interaction parameter between components i and j, which is given by:

[0114]

[0115] Model parameters v,Liq A and v,Liq B is estimated from experimental thermodynamic data and liquid-related phase boundary data.

[0116] The CALPHAD method was used to thermodynamically optimize the phase diagram of the Sn-Bi-Zn system. The optimized thermodynamic parameters and thermodynamic model are listed in Table 5. The trial-and-error method was used to assign values and optimize the calculation according to the thermodynamic data until it was basically consistent with the phase diagram and thermodynamic data, and the liquid phase projection surface of the Sn-Bi-Zn system was obtained, as shown in Table 5. Figure 2 As shown in Figure 1, the presence of a eutectic point and the temperature range of the eutectic point in the Sn-Bi-Zn system can be determined based on the liquidus projection surface of the Sn-Bi-Zn system. The calculation principle of the liquidus projection surface is to calculate the relationship between the binary zero-variable reaction and temperature change with the addition of a third component and the change in composition, thereby obtaining a ternary liquidus projection diagram. The composition and ratio of the eutectic point are calculated using the thermodynamic lever principle.

[0117] Table 5

[0118]

[0119]

[0120] In step 6, the liquidus projection of the Sn-Bi-Zn system was obtained, revealing the presence of a eutectic point. The composition ratio and eutectic temperature of the eutectic point were analyzed to be: Sn:Bi:Zn = (20.76-34.09):(49.54-55.31):(10.64-14.06) and 128.68-135.76°C, respectively. Thus, the composition ratio of the bismuth-containing alloy welding material selected from the Sn-Bi-Zn system was: Sn:Bi:Zn = (20.76-34.09):(49.54-55.31):(10.64-14.06).

[0121] Differential scanning calorimetry (DSC) was used to verify the results. The experimental results showed that the eutectic temperature of Sn:Bi:Zn was 133.50℃ with a very small error.

[0122] Step 7: Optimize the structure of the selected bismuth-containing alloy welding material and calculate its mechanical properties using the stress-strain method, including calculating its hardness, and calculate its electrical conductivity using the metal DC conductivity formula.

[0123] Step 7.1, use formula (18) to calculate the hardness of the screened Sn-Bi-Zn ternary crystal structure. The formula for hardness is as follows:

[0124] H V =0.92K -1.137 G 0.708 (18)

[0125] k is a ratio, k = B / G, B and G represent the bulk modulus and shear modulus respectively. B and G are calculated by the stress-strain method to calculate the elastic constants (C 11 ,C 12 ,C 44 ) is further obtained, the formula is as follows:

[0126]

[0127]

[0128]

[0129] Among them, B v and G v are the bulk modulus and shear modulus calculated by the Voigt model, B R is the bulk modulus calculated by the Reuss model. It is further converted into the final required B and G using the Hill model. The corresponding conversion formula is as follows:

[0130]

[0131]

[0132] The hardness of the selected bismuth-containing alloy welding material was 14.01 HBW. The hardness was tested by a microhardness tester, and the experimental value was 14.10 HBW, with a very small error range.

[0133] In step 7.2, the conductivity of the selected bismuth-containing alloy welding material is obtained using the formula for the DC conductivity of metals. The formula is as follows:

[0134]

[0135] Where n is the total charge density of conduction electrons, is the effective mass of a free electron, τ f is the relaxation time. Where n is obtained from the following formula:

[0136]

[0137] Where N is the number of conductive charges, and the calculation formula is:

[0138]

[0139] The formula for calculating the effective mass of a free electron is:

[0140]

[0141] The conductivity of the screened bismuth-containing alloy welding material was 2.89MS / m. The conductivity was tested by a high-precision Seebeck coefficient and resistivity tester, and the experimental value was 2.99MS / m, with a very small error range.

[0142] Example 2

[0143] In this embodiment, a method for screening bismuth-containing alloy welding materials comprises the following steps:

[0144] Step 1: Obtain binary crystal structures existing in the Sn-Bi-Ag system based on currently available databases and relevant literature reports, including Sn-Bi binary crystal structure, Bi-Ag binary crystal structure, and Sn-Ag binary crystal structure. Among them, the Sn-Bi-Ag system refers to a crystal structure containing three elements: Sn, Bi, and Ag; the Sn-Bi binary crystal structure refers to a binary crystal structure containing two elements: Bi and Sn; the Bi-Ag binary crystal structure refers to a binary crystal structure containing two elements: Bi and Ag; and the Sn-Ag binary crystal structure refers to a binary crystal structure containing two elements: Sn and Ag.

[0145] Step 2: Using the first-principles calculation method based on density functional theory, the initial Sn-Bi binary crystal structure, Bi-Ag binary crystal structure, and Sn-Ag binary crystal structure are subjected to low-precision structural optimization by Vasp software. Then, high-precision structural optimization is performed on the low-precision optimized Sn-Bi binary crystal structure, Bi-Ag binary crystal structure, and Sn-Ag binary crystal structure respectively. Based on the high-precision optimized Sn-Bi binary crystal structure, Bi-Ag binary crystal structure, and Sn-Ag binary crystal structure, basic phase information is calculated, including formation enthalpy. The calculation results are shown in Table 1. Step 2 specifically includes:

[0146] In step 2.1, selecting appropriate key parameters helps improve the accuracy and efficiency of the calculation. The selection of the cutoff energy and the density of the k-point mesh is crucial. A k-point mesh with a precision of 0.03 was generated using Vaspkit function 102. The cutoff energy was set to 1.5 times the element ENMAX in the POTCAR file.

[0147] Step 2.2: First, set the parameters “ISIF=3, IBRION=2” and perform low-precision structure optimization on the Sn-Bi binary crystal structure, Bi-Ag binary crystal structure, and Sn-Ag binary crystal structure respectively. The energy convergence criterion is 10 -6 eV, the force convergence criterion is Reach the convergence criterion.

[0148] Step 2.3: After the low-precision structure optimization is completed, the high-precision structure optimization is performed again for the Sn-Bi binary crystal structure, Bi-Zn binary crystal structure, and Sn-Zn binary crystal structure after the low-precision structure optimization. The energy convergence criterion is 10 -8 eV, the force convergence criterion is

[0149] Step 2.4: Based on the high-precision optimized Sn-Bi binary crystal structure, Bi-Ag binary crystal structure, and Sn-Ag binary crystal structure, the formation enthalpy of each binary crystal structure is calculated using the formation enthalpy calculation formula. Taking the Sn-Bi binary crystal structure as an example, the formation enthalpy calculation formula is shown in formula (1).

[0150]

[0151] Where ΔH represents the formation enthalpy, E total represents the total energy of the Sn-Bi binary crystal structure, E Bi and E Sn are the energies of elemental Bi and Sn, respectively. x and y are the atomic numbers of elemental Bi and Sn in the Sn-Bi binary crystal structure, respectively.

[0152] Step 3: Based on the high-precision optimized Sn-Bi binary crystal structure, Bi-Ag binary crystal structure, and Sn-Ag binary crystal structure, use Phonopy software to calculate the phonon spectrum of the Sn-Bi binary crystal structure, Bi-Ag binary crystal structure, and Sn-Ag binary crystal structure, respectively. The details are as follows:

[0153] Taking the Bi-Ag binary crystal structure as an example, based on the highly optimized Bi-Ag binary crystal structure, the Phonopy software was used to expand it, generating a SPOCAR file. Based on the symmetry of the Bi-Ag binary crystal structure, supercells with different displacements were generated. The more complex the symmetry, the greater the number of supercells with different displacements, and the greater the computational effort. With the parameters "ISIF = 2, IBRION = 8," the supercells with different displacements were calculated sequentially.

[0154] Step 4: Based on the quasi-harmonic approximation method, i.e., the QHA method, the thermal properties of the selected Sn-Bi binary crystal structure, Bi-Ag binary crystal structure, and Sn-Ag binary crystal structure with no imaginary frequency in the phonon spectrum are calculated. The specific steps are as follows:

[0155] Step 4.1, based on the Sn-Bi binary crystal structure, Bi-Ag binary crystal structure, and Sn-Ag binary crystal structure with no imaginary frequency in the phonon spectrum, perform variable volume energy and volume calculation. Specifically:

[0156] Phonon spectra of the Sn-Bi binary crystal structure, Bi-Ag binary crystal structure, and Sn-Ag binary crystal structure were calculated at volume ratios of 0.97, 0.98, 0.99, 1.00, 1.01, 1.02, and 1.03, and the corresponding thermal properties were obtained using the quasi-harmonic approximation method. The thermal properties refer to the Helmholtz energy.

[0157] The Helmholtz energy is decomposed into three cumulative contributions. As shown in formula (2):

[0158] F(V,T)=E c (V)+F vib (V,T)+F el (V,T) (2)

[0159] Where F(V,T) represents the Helmholtz energy as a function of temperature T and volume V; E c is the static total energy of 0K directly output by the quasi-harmonic approximation method based on the first principle; F vib is the vibrational free energy; F el is the contribution of hot electrons to the Helmholtz energy.

[0160] F vib (V,T) is calculated from the phonon DOS (p-DOS) as shown in formula (3):

[0161]

[0162] Where K B is the Boltzmann constant, g(ω,V) is the phonon state density as a function of the phonon frequency ω, is the simplified Planck constant. The contribution of hot electron excitation F el (V, T) is calculated by MermIn statistics, as shown in formula (4):

[0163] F el (V,T)=E el (V,T)-TS el (V,T) (4)

[0164] Electron entropy Sel Calculated by the following formula:

[0165] 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)

[0166] The hot electron energy is calculated by the following formula:

[0167]

[0168] where n(ε,V) is the electron density of states (e-DOS) as a function of the single electron energy ε, f is the Fermi function, and ε F It's Fermi energy.

[0169] The modified Birch-Murnaghan equation of state (EOS) is then used to fit the Helmholtz energy at a given temperature for seven given volumes, as shown in Equation (7):

[0170] F(V,T)=a+bV -2 / 3 +cV -4 / 3 +dV -2 +eV -8 / 3 (6)

[0171] 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:

[0172]

[0173] From the calculated equilibrium volume Veq(T), the volumetric thermal expansion coefficient (β(T)) is calculated as follows:

[0174]

[0175] The relationship between the average linear expansion coefficients α(T) and β(T) is α(T)=β(T) / 3.

[0176] Adiabatic modulus B T (V,T) is calculated by the following formula:

[0177]

[0178] For the main input data of thermodynamic modeling, entropy is derived as:

[0179]

[0180] Temperature-dependent enthalpy (H(V eq ,T)) is calculated by the following formula:

[0181] H(V eq ,T)=U(V eq ,T)=F(V eq ,T)+TS(V eq ,T) (11)

[0182] Where U(Veq,T) is the internal energy, which is the same as the isochoric melting (C V (V eq ,T)) has the following relationship:

[0183]

[0184] The isobaric heat capacity is obtained from the following formula:

[0185] C P (V eq ,T)=C V (V eq ,T)+V eq TB T (V eq ,T)(β(T)) 2 (13)

[0186] Step 5: Based on the thermal properties of the Sn-Bi binary crystal structure, the Bi-Ag binary crystal structure, and the Sn-Ag binary crystal structure calculated above, combined with the CALPHAD model, a thermodynamic model of the Sn-Bi-Ag system is established. The CALPHAD model used is described as follows:

[0187] The Gibbs energy of a compound at different temperatures is shown below:

[0188]

[0189] Where a, b, c, d, e and f are model parameters, which are evaluated from the thermodynamic data calculated by the first-principles quasi-harmonic approximation method described above. SER The enthalpy of the most stable element at 298.15K and 1 bar is used as the reference state. The Gibbs energy expression of the liquid phase is:

[0190]

[0191] where y i is the mole fraction of component i in the liquid phase, xs G L is the excess Gibbs energy phase, Represents the Gibbs energy of the pure liquid phase. Excess Gibbs energy xs G LThe form is:

[0192]

[0193] in is the vth-order interaction parameter between components i and j, which is given by:

[0194]

[0195] Model parameters v,Liq A and v,Liq B is estimated from experimental thermodynamic data and liquid-related phase boundary data.

[0196] The CALPHAD method was used to thermodynamically optimize and calculate the phase diagram of the Sn-Bi-Ag system. The optimized thermodynamic parameters and thermodynamic model are shown in Table 6. The trial-and-error method was used to assign values and optimize the calculation according to the thermodynamic data until it was basically consistent with the phase diagram and thermodynamic data. The liquid phase projection surface of the Sn-Bi-Ag system was obtained, as shown in Table 6. Figure 3 As shown in Figure 1, the presence of a eutectic point and the temperature range of the eutectic point in the Sn-Bi-Ag system can be determined based on the liquidus projection surface. The calculation principle of the liquidus projection surface is to calculate the relationship between the binary zero-variable reaction and temperature as the third component is added and the composition changes, thereby obtaining a ternary liquidus projection diagram. The composition and ratio of the eutectic point are calculated using the thermodynamic lever principle.

[0197] Table 6

[0198]

[0199]

[0200] In step 6, the liquidus projection of the Sn-Bi-Ag system was obtained, revealing the presence of a eutectic point. The composition ratio and temperature of the eutectic point were analyzed to be: Sn:Bi:Ag = (32.51-38.54):(44.70-52.68):(13.79-16.88) and 132.87-140.65°C, respectively. This indicates that the composition ratio of the bismuth-containing alloy welding material selected from the Sn-Bi-Ag system is: Sn:Bi:Ag = (32.51-38.54):(44.70-52.68):(13.79-16.88).

[0201] Differential scanning calorimetry (DSC) was used to verify the results. The experimental results showed that the eutectic temperature of Sn:Bi:Ag was 137.70℃ with a very small error.

[0202] Step 7: Optimize the structure of the selected bismuth-containing alloy welding material and calculate its mechanical properties using the stress-strain method, including calculating its hardness, and calculate its electrical conductivity using the metal DC conductivity formula.

[0203] Step 7.1, use formula (18) to calculate the hardness of the screened Sn-Bi-Ag ternary crystal structure. The formula for hardness is as follows:

[0204] H V =0.92K -1.137 G 0.708 (18)

[0205] k is a ratio, k = B / G, B and G represent the bulk modulus and shear modulus respectively. B and G are calculated by the stress-strain method to calculate the elastic constants (C 11 ,C 12 ,C 44 ) is further obtained, the formula is as follows:

[0206]

[0207]

[0208]

[0209] Among them, B v and G v are the bulk modulus and shear modulus calculated by the Voigt model, B R is the bulk modulus calculated by the Reuss model. It is further converted into the final required B and G using the Hill model. The corresponding conversion formula is as follows:

[0210]

[0211]

[0212] The hardness of the selected bismuth-containing alloy welding material was 28.58 HBW. A microhardness tester showed a hardness value of 28.60 HBW, with a very small error range.

[0213] In step 7.2, the conductivity of the selected bismuth-containing alloy welding material is obtained using the formula for the DC conductivity of metals. The formula is as follows:

[0214]

[0215] Where n is the total charge density of conduction electrons, is the effective mass of a free electron, τ f is the relaxation time. Where n is obtained from the following formula:

[0216]

[0217] Where N is the number of conductive charges, and the calculation formula is:

[0218]

[0219] The formula for calculating the effective mass of a free electron is:

[0220]

[0221] The conductivity of the screened bismuth-containing alloy welding material was 2.50MS / m. The conductivity was tested by a high-precision Seebeck coefficient and resistivity tester, and the experimental value was 2.44MS / m, with a very small error range.

[0222] The above describes an embodiment of the method of the present invention in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiment. Various modifications can be made according to the purpose of the invention. Any parameter changes or calculation simplifications made according to the principles of the technical solution of the present invention, as long as they meet the purpose of the invention and do not deviate from the principles and concepts of the method for screening bismuth-containing alloy welding materials and bismuth-containing alloy welding materials of the present invention, are within the scope of protection of the present invention.

Claims

1. A method for screening bismuth-containing alloy welding materials, characterized in that: Includes the following: Step 1, obtaining the binary crystal structure existing in the Sn-Bi-TM system, where TM represents one of Sb, Ag, Zn, and Cu; Step 2: Using the first principles based on density functional theory to perform low-precision to high-precision structural optimization on each binary crystal structure, and calculate the basic phase information of each binary crystal structure; Step 3, based on each binary crystal structure after high-precision optimization, calculating the phonon spectrum of each binary crystal structure; Step 4, calculating the thermal properties of each binary crystal structure based on the quasi-harmonic approximation method to obtain thermodynamic data; Step 5, using the thermodynamic data obtained in step 4 to evaluate the CALPHAD model parameters and establish a thermodynamic model for the Sn-Bi-TM system; Step 6: Based on the thermodynamic model, the liquid phase projection surface of each binary crystal structure is obtained, and the eutectic point and temperature are found based on the liquid phase projection surface to screen out the bismuth-containing alloy welding material.

2. The method for screening bismuth-containing alloy welding materials according to claim 1, characterized in that: The step 3 includes: setting parameters "ISIF=2, IBRION=8", calculating the phonon spectrum of each binary crystal structure one by one using the Phonopy finite displacement method, and screening out the binary crystal structure whose phonon spectrum has no imaginary frequency.

3. The method for screening bismuth-containing alloy welding materials according to claim 1, characterized in that: In step 5, the CALPHAD model is as follows: The Gibbs energy of a compound at different temperatures is shown below: where a, b, c, d, e and f are model parameters evaluated from thermodynamic data calculated by first-principles quasi-harmonic methods, H SER The enthalpy of the most stable element at 298.15K and 1 bar is used as the reference state.

4. The method for screening bismuth-containing alloy welding materials according to claim 3, characterized in that: The step 5 further comprises: The Gibbs energy expression of the liquid phase is: where y i is the mole fraction of component i in the liquid phase, xs G L is the excess Gibbs energy phase, Represents the Gibbs energy of the pure liquid phase, excess Gibbs energy xs G L The form is: in is the vth-order interaction parameter between components i and j, which is given by: Model parameters v,Liq A and v,Liq B is estimated from experimental thermodynamic data and liquid-related phase boundary data.

5. The method for screening bismuth-containing alloy welding materials according to claim 4, characterized in that: In step 5, the thermodynamic model of the Sn-Bi-Zn system is: The thermodynamic model of the Sn-Bi-Ag system is:

6. The method for screening bismuth-containing alloy welding materials according to claim 5, characterized in that: The method further includes step 7, which involves optimizing the structure of the selected bismuth-containing alloy welding material, calculating the mechanical properties using a stress-strain method, including calculating the hardness, and calculating the electrical conductivity using a metal DC electrical conductivity formula.

7. Bismuth-containing alloy welding material, characterized in that: The bismuth-containing alloy welding material is obtained by screening using the method for screening bismuth-containing alloy welding material according to any one of claims 1 to 6.

8. The bismuth-containing alloy welding material according to claim 7, characterized in that: Including bismuth-containing alloy welding materials with a composition ratio of Sn:Bi:Ag of (32.51-38.54):(44.70-52.68):(13.79-16.88), and bismuth-containing alloy welding materials with a composition ratio of Sn:Bi:Zn of (20.76-34.09):(49.54-55.31):(10.64-14.06).

9. The bismuth-containing alloy welding material according to claim 8, characterized in that The eutectic temperature of the bismuth-containing alloy welding material with the screened Sn:Bi:Zn composition ratio of (20.76-34.09):(49.54-55.31):(10.64-14.06) is 128.68-135.76°C; the eutectic temperature of the bismuth-containing alloy welding material with the screened Sn:Bi:Ag composition ratio of (32.51-38.54):(44.70-52.68):(13.79-16.88) is 132.87-140.65°C.

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