Method for screening welding materials of ultra-low melting point eutectic alloys based on first principles

Abstract

The present invention discloses a method for screening ultra-low melting point eutectic alloy welding materials based on first principles, including obtaining the crystal structure existing in the Sn-In-TM system, the first principle calculation method based on density functional theory, high-precision structural relaxation to obtain the basic phase information of each crystal structure in the Sn-In-TM system, and calculating the thermodynamic properties of the crystal structure in the Sn-In-TM system, and further combining the CALPHAD model to establish a thermodynamic model of the Sn-In-TM system, and analyzing the composition and temperature of the eutectic point. An ultra-low melting point eutectic alloy welding material is screened out: its composition ratio is Sn: In: Bi = (18.15-22.76): (30.57-33.54): (41.58-45.31). The eutectic point temperature of this ultra-low melting point eutectic alloy welding material is 41.6-45.7 ° C, and the ratio of the composition of the ultra-low melting point eutectic alloy welding material is discovered for the first time, with the advantages of ultra-low melting point, high powder making quality, and no bonding phenomenon.

Description

Technical Field

[0001] The present invention relates to the technical field of welding material screening, and in particular to a method for screening ultra-low melting point eutectic alloy welding materials based on first principles. Background Art

[0002] In electronic packaging technology, solder alloys are used as solders to connect electronic components. They form mechanical connections that can conduct electricity and heat with device pins or circuit wires to achieve the stability of the performance of electronic products during service. Therefore, for circuits formed by packaging and assembly, the performance of solder alloys plays a vital role in the operation of the entire circuit. In microelectronic connections, the research on solder alloy materials mainly includes low melting point, excellent fluidity and wettability, sufficient conductivity, corrosion resistance and mechanical strength. At present, the main lead-free solders studied in China are Sn-Ag, Sn-Cu, Sn-Bi, Sn-Zn, Sn-In, etc. These lead-free solders are competent for most purposes. However, when packaging and connecting temperature-sensitive materials, such as electronic components with poor heat resistance, temperature sensors and other equipment, it is necessary to solder at low temperatures. At this time, the solder alloy shows limitations, so it is urgent to find new low-melting point eutectic welding materials.

[0003] Developing solder alloys is an expensive and time-consuming task, so new methods need to be found to improve efficiency. Using phase diagram calculation (CALPHAD) technology to optimize the calculation of new lead-free solder systems and establish a phase diagram thermodynamic database of solder systems to guide the composition design of new lead-free solders is another feature of today's lead-free solder research and development. Here, we created this method, through high-throughput first-principles calculations combined with the CALPHAD model, to establish a thermodynamic model of the ternary alloy system, obtain the liquidus surface projection diagram of the ternary system, and further screen the ternary alloy system with an ultra-low eutectic point. Finally, the accuracy of the calculation is verified by experiment, which greatly saves experimental costs and shortens the product development cycle. Summary of the invention

[0004] The method for screening ultra-low melting point eutectic alloy welding materials based on first principles of the present invention comprises the following contents:

[0005] Step 1, obtaining a binary crystal structure existing in a Sn-In-TM system, wherein TM represents one of Sb, Ag, Zn, Bi, and Cu;

[0006] Step 2, respectively conduct convergence tests on the cutoff energy and the k-point mesh density, select the cutoff energy corresponding to the lowest energy point, and select the k-point mesh density corresponding to the lowest energy point;

[0007] Step 3: Based on the first principle calculation method of density functional theory, low-precision structural optimization is performed on each binary crystal structure, and the energy convergence criterion is 10 -6 eV, the force convergence criterion is Then, each binary crystal structure after low-precision optimization is subjected to high-precision structural optimization, and the energy convergence criterion is 10 -8 eV, the force convergence criterion is After reaching the convergence standard, the basic phase information is calculated based on each binary crystal structure after high-precision optimization;

[0008] Step 4, based on each binary crystal structure after high-precision optimization, calculating the phonon spectrum of each binary crystal structure, and screening the binary crystal structure whose phonon spectrum has no imaginary frequency;

[0009] Step 5, based on the quasi-harmonic approximation method, the thermal properties of each binary crystal structure with no imaginary frequency in the screened phonon spectrum are calculated respectively;

[0010] Step 6, based on the calculated thermal properties of each binary crystal structure, thermodynamic data is obtained, and the CALPHAD model is combined to optimize the CALPHAD model parameters according to the thermodynamic data to establish a thermodynamic model of the Sn-In-TM system;

[0011] Step 7, based on the thermodynamic model of the Sn-In-TM system, obtain the liquid phase projection surface of the Sn-In-TM system, analyze the composition ratio and temperature of the eutectic point, and screen out the ultra-low melting point eutectic alloy welding material.

[0012] A preferred implementation manner of the present invention is that step 2 specifically includes: when testing the cutoff energy, selecting a k-point grid density of 4*4*4, fixing other parameters, and testing the energies corresponding to different cutoff energies of 150, 200, 250, 300, 350, 400, 450, and 500 respectively, and selecting the truncation energy of 450 corresponding to the lowest energy point; then testing the k-point grid density, selecting the truncation energy of 450, fixing other parameters, and testing the energies under different k-point grid densities of 4*4*4, 6*6*6, 8*8*8, and 10*10*10 respectively, and selecting the k-point grid density of 8*8*8 corresponding to the lowest energy point.

[0013] A preferred embodiment of the present invention is that step 3 specifically comprises:

[0014] Step 3.1, set the parameter optimization parameters “ISIF=3, IBRION=2”, perform low-precision structural optimization on the Sn-In binary crystal structure, In-Bi binary crystal structure, and Sn-Bi binary crystal structure, respectively, and the energy convergence criterion is 10 -6 eV, the force convergence criterion is

[0015] Step 3.2: After the low-precision structure optimization is completed, the high-precision structure optimization is performed again based on the Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure after the low-precision structure optimization. The energy convergence criterion is 10 -8 eV, the force convergence criterion is After two structural optimizations, the convergence standard was not reached. The optimization parameters were modified to "ISIF = 2, IBRION = 1", and the optimization was continued until the convergence standard was reached.

[0016] Step 3.3, based on the structural energy after high-precision structural optimization, respectively calculate the basic phase information, the basic phase information includes formation enthalpy, and use the formation enthalpy calculation formula to respectively calculate the formation enthalpy of each binary crystal structure.

[0017] A preferred embodiment of the present invention is that step 4 specifically comprises:

[0018] Step 4.1, set the parameters "ISIF = 2, IBRION = 8", use the Phonopy finite displacement method to calculate the phonon spectrum of each binary crystal structure one by one, and there are imaginary frequencies at the high symmetry points of the phonon spectrum;

[0019] Step 4.2, after high-precision structural optimization, the binary crystal structures are optimized again, and the force convergence criterion is raised to The energy convergence criterion remains unchanged, and each binary crystal structure is expanded by 2*2*2. The corresponding high symmetry k-point setting is reduced by half, and the phonon spectrum calculation is performed again until the phonon spectrum has no imaginary frequency.

[0020] A preferred embodiment of the present invention is that step 6 comprises:

[0021] The CALPHAD model is as follows:

[0022] The Gibbs energy of a compound at different temperatures is shown below:

[0023]

[0024] where a, b, c, d, e and f are model parameters evaluated from the thermodynamic data obtained from the first-principles quasi-harmonic calculations described above, H SER The enthalpy of the most stable element at 298.15K and 1 bar is used as the reference state.

[0025] A preferred embodiment of the present invention is that step 6 further comprises:

[0026] The Gibbs energy of the liquid phase is expressed as:

[0027]

[0028] 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;

[0029] Excess Gibbs Energy xs G L The form is:

[0030]

[0031] in is the vth-order interaction parameter between components i and j and is given by:

[0032]

[0033] Model parameters v,Liq A and v,Liq B is estimated from thermodynamic data and liquid-related phase boundary data.

[0034] A preferred embodiment of the present invention is that the thermodynamic model of the Sn-In-Bi system is:

[0035]

[0036] A preferred embodiment of the present invention is that the composition ratio of Sn:In:Bi screened from the Sn-In-Bi system is (18.15-22.76):(30.57-33.54):(41.58-45.31), and the eutectic temperature is 41.6-45.7°C.

[0037] The present invention establishes a thermodynamic model of the Sn-In-TM system based on high-throughput first-principle calculations combined with the CALPHAD model. The ternary alloy with a low melting point eutectic composition is screened out, and the error range is very small through experimental verification, which improves the research and development efficiency of new bismuth-containing ternary alloy welding materials and reduces research and development costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Attached Figure 1 This is a flow chart of a method for screening ultra-low melting point eutectic alloy welding materials based on first principles of the present invention;

[0039] Attached Figure 2 This is the result of the test on the convergence of the cutoff energy of the Sn-Bi binary crystal structure;

[0040] Attached Figure 3 This is the result of the k-point mesh density convergence test of the Sn-Bi binary crystal structure;

[0041] Attached Figure 4 This is the result of the test on the truncation energy convergence of the Sn-In binary crystal structure;

[0042] Attached Figure 5 This is the result of the k-point mesh density convergence test of the Sn-In binary crystal structure;

[0043] Attached Figure 6 It is the liquid phase projection surface of Sn-In-Bi system;

[0044] Attached Figure 7 It is the liquid phase projection surface of Sn-In-Sb system;

[0045] Attached Figure 8 The conductivity of Sn-In-Bi system changes with temperature;

[0046] Attached Fig. 9 The conductivity of the Sn-In-Bi system changes with the Bi content. DETAILED DESCRIPTION

[0047] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0048] The present invention obtains the crystal structures existing in the Sn-In-TM system based on currently open databases and relevant literature reports, and obtains a total of 139 crystal structures, wherein TM represents one of Sb, Ag, Zn, Bi, and Cu. Open databases include Materials Project, OQMD, Springer Materials, ICSD, and NIST. The Sn-Bi-TM system refers to a crystal structure containing one or two of the three elements Sn, In, and TM.

[0049] (1) Based on the high-throughput first-principles calculation of density functional theory, low-precision and high-precision structural optimization of 139 crystal structures were performed, and the basic phase information of 139 crystal structures in the Sn-In-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.

[0050] Table 1

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] (2) Based on the binary crystal structure after high-precision structural optimization, the phonon spectrum of each binary crystal structure was calculated using Phonopy software.

[0057] (3) Based on the quasi-harmonic approximation method, namely the QHA method, the thermal properties of single elements and binary crystal structures are calculated to obtain thermodynamic data.

[0058] (4) The CALPHAD model parameters were evaluated based on the thermodynamic data calculated by the quasi-harmonic approximation method based on the first principles. Finally, a thermodynamic model of the Sn-In-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. The ultra-low melting point eutectic alloy welding material was screened out from the Sn:In:Bi system with a composition ratio of Sn:In:Bi=21.15:33.54:45.31.

[0059] Compared with other alloy welding materials, the advantages of ultra-low melting point eutectic welding materials screened by calculation and verified by experiments are as follows:

[0060] (1) The composition ratio of Sn-In-Bi ultra-low melting point eutectic welding material is Sn:In:Bi=(18.15-22.76):(30.57-33.54):(41.58-45.31), which is the first discovery.

[0061] (2) The melting point of Sn-In-Bi ultra-low melting point eutectic welding material is ultra-low, at 41.6-45.7℃.

[0062] (3) The Sn-In-Bi ultra-low melting point eutectic welding material is a eutectic alloy with no solid-liquid two-phase region, no adhesion phenomenon, easy processing and high powder quality.

[0063] The following is a method for selecting ultra-low melting point eutectic alloy welding materials from the Sn-In-Bi system to describe the specific steps of the present invention in detail. The method for selecting ultra-low melting point eutectic alloy welding materials from other systems is the same as the method for selecting ultra-low melting point eutectic alloy welding materials from the Sn-In-Bi system.

[0064] Embodiment 1

[0065] As attached Figure 1 As shown, in this embodiment, the method for screening ultra-low melting point eutectic alloy welding materials based on first principles is as follows:

[0066] Step 1, based on currently open databases and relevant literature reports, obtain the binary crystal structures existing in the Sn-In-Bi system, including the Sn-In binary crystal structure, the In-Bi binary crystal structure and the Sn-Bi binary crystal structure. Among them, the Sn-In-Bi system refers to a crystal structure containing one or two of the three elements Sn, In and Bi, the Sn-In binary crystal structure refers to a binary crystal structure containing two elements Sn and In, the Bi-In binary crystal structure refers to a binary crystal structure containing two elements Bi and In, and the Sn-Bi binary crystal structure refers to a binary crystal structure containing two elements Sn and Bi.

[0067] Step 2: To ensure the accuracy and efficiency of the calculation, the parameter settings need to be tested for convergence. Convergence tests are performed on the cutoff energy and k-point grid density. When testing the cutoff energy, select a k-point grid density of 4*4*4, fix other parameters, and test the corresponding energies at different cutoff energies of 150, 200, 250, 300, 350, 400, 450, and 500. Figure 2 This is the result of the test on the truncation energy convergence of the Sn-Bi binary crystal structure. Figure 4 This is the result of the truncation energy convergence test for the Sn-In binary crystal structure. The truncation energy corresponding to the lowest energy point is selected as 450. Then the k-point grid density is tested. The truncation energy is selected as 450. Other parameters are fixed. The energy under different k-point grid densities of 4*4*4, 6*6*6, 8*8*8, and 10*10*10 is tested respectively. Figure 3 This is the result of the k-point mesh density convergence test of the Sn-Bi binary crystal structure. Figure 5 This is the result of the k-point mesh density convergence test of the Sn-In binary crystal structure. The k-point mesh density corresponding to the lowest energy point is 8*8*8.

[0068] Step 3, based on the first principle calculation method of density functional theory, the initial Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure are optimized with low precision by Vasp software, and then the low-precision optimized Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure are optimized with high precision respectively, and the basic phase information is calculated based on the high-precision optimized Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure respectively, and the basic phase information includes the formation enthalpy, and the calculation results are shown in Table 1. Step 3 specifically includes:

[0069] Step 3.1, first set the parameters "ISIF = 3, IBRION = 2". ISIF = 3, that is, select full relaxation optimization of each binary crystal structure, optimize the atomic position and volume of each binary crystal structure. IBRION = 2, that is, select the conjugate gradient algorithm for calculation, and perform low-precision structural optimization on the Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure respectively, and the energy convergence criterion is 10 -6 eV, the force convergence criterion is Vasp structural optimization ultimately has two convergence criteria, namely the convergence criteria of energy and force. Low-precision structural optimization means that the convergence standards of energy and force are lower, while high-precision structural optimization means that the convergence standards of energy and force are higher.

[0070] Step 3.2: After the low-precision structure optimization is completed, the high-precision structure optimization is performed again based on the Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure after the low-precision structure optimization. The energy convergence criterion is 10 -8 eV, the force convergence criterion is After two structural optimizations, the convergence standard was not reached. Modify the optimization parameters to "ISIF = 2, IBRION = 1", ISIF = 2, that is, select atomic relaxation to optimize each binary crystal structure, and only optimize the atomic position of each binary crystal structure, IBRION = 1, that is, select the quasi-Newton gradient algorithm for calculation, and continue to optimize until the convergence standard is reached;

[0071] Step 3.3, based on the structure after high-precision structural optimization, the formation enthalpy calculation formula is used to calculate the formation enthalpy of the Sn-In binary crystal structure, the In-Bi binary crystal structure, and the Sn-Bi binary crystal structure, respectively, as the parameters of the CALPHAD model. Taking the Sn-In binary crystal structure as an example, as shown in formula (1):

[0072]

[0073] Where: ΔH represents the enthalpy of formation, E total represents the total energy of the Sn-In binary crystal structure, E In and E Sn Represent the energy of simple In and Sn respectively. x and y represent the number of atoms of simple In and Sn in the Sn-In binary crystal structure respectively.

[0074] Step 4: Based on the highly-precision optimized Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure, use Phonopy software to calculate the phonon spectrum. The details are as follows:

[0075] Step 4.1, set the parameters "ISIF = 2, IBRION = 8", use the Phonopy finite displacement method to calculate the phonon spectra of the Sn-In binary crystal structure, the In-Bi binary crystal structure and the Sn-Bi binary crystal structure one by one, and there are imaginary frequencies at the high symmetry points of the phonon spectrum.

[0076] Step 4.2, the Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure after high-precision structural optimization are optimized again, and the force convergence criterion is increased to The convergence criterion of energy remains unchanged. The Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure are expanded by 2*2*2, and the corresponding high symmetry k-point setting is reduced by half, and the phonon spectrum calculation is performed again until the phonon spectrum has no imaginary frequency. The phonon spectrum without imaginary frequency is selected and the thermal properties are calculated using the quasi-harmonic approximation method to ensure the accuracy of the calculation.

[0077] Step 5, based on the quasi-harmonic approximation method of the first principles, the thermal properties of the selected Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure with no imaginary frequency in the phonon spectrum are calculated respectively. The details are as follows:

[0078] The variable volume energy volume calculation is performed using the Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure with no imaginary frequency in the phonon spectrum.

[0079] The phonon spectra of the Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure at volumes of 0.97, 0.98, 0.99, 1.00, 1.01, 1.02 and 1.03 are calculated one by one.

[0080] The corresponding thermal properties are obtained based on the quasi-harmonic approximation method of the first principles, and the thermal properties refer to the Helmholtz energy.

[0081] The Helmholtz energy is decomposed into three cumulative contributions. As shown in formula (2):

[0082] F(V,T)=E c (V)+F vib (V,T)+F el (V,T) (2)

[0083] Where F(V,T) represents the Helmholtz energy as a function of temperature T and volume V; E c is the 0K static total energy 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.

[0084] F vib (V,T) is calculated from the phonon DOS (p-DOS) as:

[0085]

[0086] 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.

[0087] The contribution of hot electron excitation F el (V,T) is calculated by MermIn statistics:

[0088] F el (V,T)=E el (V,T)-TS el (V,T) (4)

[0089] Electron entropy S el Calculated by the following formula:

[0090] 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)

[0091] The hot electron energy is calculated by the following formula:

[0092]

[0093] where n(ε,V) is the electron density of states (e-DOS) of a single electron with energy ε, f is the Fermi function, ε F It's Fermi energy.

[0094] The modified Birch-Murnaghan equation of state (EOS) was then used to fit the Helmholtz energies at seven given volumes and temperatures:

[0095] F(V,T)=a+bV -2 / 3 +cV -4 / 3 +dV -2 +eV -8 / 3 (7)

[0096] 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:

[0097]

[0098] Calculated equilibrium volume V eq (T), the volume thermal expansion coefficient (β(T)) is calculated by the following formula:

[0099]

[0100] The relationship between the average linear expansion coefficients α(T) and β(T) is α(T)=β(T) / 3.

[0101] Adiabatic modulus B T (V,T) is calculated by the following formula:

[0102]

[0103] The main input data for thermodynamic modeling, entropy, can be derived as:

[0104]

[0105] Temperature dependence of enthalpy (H(V eq ,T)) can be calculated by the following formula:

[0106] H(V eq ,T)=U(V eq ,T)=F(V eq ,T)+TS(V eq ,T) (12)

[0107] Where U(V eq ,T) is the internal energy, which is the same as the isochoric melting (C V (V eq ,T)) has the following relationship:

[0108]

[0109] The isobaric heat capacity can be obtained from the following formula (14):

[0110] C P (V eq ,T)=C V (V eq ,T)+V eq TB T (V eq ,T)(β(T)) 2 (14)

[0111] Step 6: Based on the thermal properties of the Sn-In binary crystal structure, the In-Bi binary crystal structure, and the Sn-Bi binary crystal structure calculated above, and combined with the CALPHAD model, a thermodynamic model of the Sn-In-Bi system is established.

[0112] The CALPHAD model is as follows:

[0113] The Gibbs energy of a compound at different temperatures is shown below:

[0114]

[0115] where a, b, c, d, e and f are model parameters evaluated from the thermodynamic data obtained from the first-principles quasi-harmonic calculations described above. SER The enthalpy of the most stable element at 298.15K and 1 bar is used as the reference state.

[0116] The Gibbs energy of the liquid phase is expressed as:

[0117]

[0118] 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.

[0119] Excess Gibbs Energy xs G L The form is:

[0120]

[0121] in is the vth-order interaction parameter between components i and j and is given by:

[0122]

[0123] Model parameters v,Liq A and v,Liq B is estimated from experimental thermodynamic data and liquid-related phase boundary data.

[0124] The CALPHAD model was used to thermodynamically optimize and calculate the Sn-In-Bi system phase diagram. The optimized thermodynamic parameters and thermodynamic model are shown in Table 2. 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-In-Bi system was obtained, as shown in Table 2. Figure 6 As shown. According to the liquid phase projection surface of the Sn-In-Bi system, it is judged whether there is a eutectic point and the temperature range of the eutectic point in the Sn-Bi-Zn system. The calculation principle of the liquid phase projection surface is: by calculating the relationship between the binary zero variable reaction and the temperature change with the addition of the third component and the change of composition, the ternary liquid phase projection diagram is obtained, and the composition and proportion of the eutectic point are calculated by the thermodynamic lever principle.

[0125] Table 2

[0126]

[0127] Step 7, according to the obtained liquid phase projection surface of the Sn-In-Bi system, it is found that there is a eutectic point, and the composition ratio and eutectic temperature of the eutectic point are analyzed as follows: Sn:In:Bi=(18.15-22.76):(30.57-33.54):(41.58-45.31) and 41.6-45.7° C. That is, the composition ratio of the ultra-low melting point eutectic alloy welding material selected from the Sn-In-Bi system is Sn:In:Bi=(18.15-22.76):(30.57-33.54):(41.58-45.31).

[0128] The conductivity of the selected ultra-low melting point eutectic alloy welding material is calculated using the metal DC conductivity formula. The formula is as follows:

[0129]

[0130] 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:

[0131]

[0132] Where N is the number of conductive charges, and the calculation formula is:

[0133]

[0134] The formula for calculating the effective mass of a free electron is:

[0135]

[0136] The conductivity of the selected ultra-low melting point eutectic alloy welding material is 8.23MS / m, and the change of conductivity with temperature and Bi composition is shown in the attached figure. Figure 8 and attached Fig. 9 shown.

[0137] Embodiment 2

[0138] This embodiment is based on the first principle method for screening ultra-low melting point eutectic alloy welding materials, the steps are as follows:

[0139] Step 1, based on currently open databases and relevant literature reports, obtain the binary crystal structures existing in the Sn-In-Sb system, including the Sn-In binary crystal structure, the In-Sb binary crystal structure and the Sn-Sb binary crystal structure. Among them, the Sn-In-Sb system refers to a crystal structure containing three elements Sn, In and Sb, the Sn-In binary crystal structure refers to a binary crystal structure containing two elements Sn and In, the In-Sb binary crystal structure refers to a binary crystal structure containing two elements In and Sb, and the Sn-Sb binary crystal structure refers to a binary crystal structure containing two elements Sn and Sb.

[0140] Step 2: To ensure the accuracy and efficiency of the calculation, the parameter settings need to be tested for convergence. Convergence tests were performed on the cutoff energy and k-point grid density respectively. When testing the cutoff energy, the k-point grid density was selected as 4*4*4, and other parameters were fixed. The corresponding energies under different cutoff energies of 150, 200, 250, 300, 350, 400, 450, and 500 were tested respectively, and the truncation energy corresponding to the lowest energy point was selected as 450. Then the k-point grid density was tested, and the truncation energy was selected as 450, and other parameters were fixed. The energies under different k-point grid densities of 4*4*4, 6*6*6, 8*8*8, and 10*10*10 were tested respectively, and the k-point grid density corresponding to the lowest energy point was selected as 8*8*8.

[0141] Step 3, based on the first principle calculation method of density functional theory, the initial Sn-In binary crystal structure, In-Sb binary crystal structure and Sn-Sb binary crystal structure are optimized with low precision by Vasp software, and then the low-precision optimized Sn-In binary crystal structure, In-Sb binary crystal structure and Sn-Sb binary crystal structure are optimized with high precision respectively, and the basic phase information is calculated based on the high-precision optimized Sn-In binary crystal structure, In-Sb binary crystal structure and Sn-Sb binary crystal structure respectively, and the basic phase information includes the formation enthalpy, and the calculated structure is shown in Table 1. Step 3 specifically includes:

[0142] Step 3.1, first set the parameter optimization parameters “ISIF = 3, IBRION = 2”, and perform low-precision structural optimization on the Sn-In binary crystal structure, In-Sb binary crystal structure, and Sn-Sb binary crystal structure, respectively. The energy convergence criterion is 10 - 6 eV, the force convergence criterion is

[0143] Step 3.2: After the low-precision structure optimization is completed, the Sn-In binary crystal structure, In-Sb binary crystal structure and Sn-Sb binary crystal structure after the low-precision structure optimization are again optimized with high precision. The energy convergence criterion is 10 -8 eV, the force convergence criterion is After two structural optimizations, the convergence standard was not reached. Modify the optimization parameters to "ISIF = 2, IBRION = 1", continue the optimization, and reach the convergence standard.

[0144] Step 3.3, based on the structural energy after high-precision structural optimization, the formation enthalpy calculation formula is used to calculate the formation enthalpy of the Sn-In binary crystal structure, the In-Sb binary crystal structure and the Sn-Sb binary crystal structure, taking the Sn-In binary crystal structure as an example, as shown in formula (1):

[0145]

[0146] Where: ΔH represents the enthalpy of formation, E total represents the total energy of the Sn-In binary crystal structure, E In and E Sn Represent the energy of simple In and Sn respectively. x and y represent the number of atoms of simple In and Sn in the Sn-In binary crystal structure respectively.

[0147] Step 4: Based on the highly-precision optimized Sn-In binary crystal structure, In-Sb binary crystal structure, and Sn-Sb binary crystal structure, use Phonopy software to calculate the phonon spectrum. The details are as follows:

[0148] Step 4.1, first set the parameters "ISIF = 2, IBRION = 8", use the Phonopy finite displacement method to calculate the phonon spectra of the Sn-In binary crystal structure, the In-Sb binary crystal structure and the Sn-Sb binary crystal structure one by one, and there are imaginary frequencies at the high symmetry points of the phonon spectrum.

[0149] Step 4.2, the Sn-In binary crystal structure, In-Sb binary crystal structure and Sn-Sb binary crystal structure after high-precision structural optimization are optimized again, and the force convergence criterion is improved to The convergence criterion of energy remains unchanged. The Sn-In binary crystal structure, In-Sb binary crystal structure and Sn-Sb binary crystal structure are expanded by 2*2*2, and the corresponding high symmetry k-point setting is reduced by half, and the phonon spectrum calculation is performed again until the phonon spectrum has no imaginary frequency.

[0150] Step 5, based on the quasi-harmonic approximation method, the thermal properties of the selected Sn-In binary crystal structure, In-Sb binary crystal structure and Sn-Sb binary crystal structure with no imaginary frequency in the phonon spectrum are calculated respectively.

[0151] The energy and volume of variable volume are calculated using the Sn-In binary crystal structure, In-Sb binary crystal structure and Sn-Sb binary crystal structure with no imaginary frequency in the phonon spectrum.

[0152] The phonon spectra of the Sn-In binary crystal structure, In-Sb binary crystal structure and Sn-Sb binary crystal structure at volumes of 0.97, 0.98, 0.99, 1.00, 1.01, 1.02 and 1.03 are calculated one by one.

[0153] The corresponding thermal properties are obtained based on the quasi-harmonic approximation method of the first principles, and the thermal properties refer to the Helmholtz energy.

[0154] The Helmholtz energy is decomposed into three cumulative contributions. As shown in formula (2):

[0155] F(V,T)=E c (V)+F vib (V,T)+F el (V,T) (2)

[0156] Where F(V,T) represents the Helmholtz energy as a function of temperature T and volume V; E c is the 0K static total energy 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.

[0157] F vib (V,T) is calculated from the phonon DOS (p-DOS) as:

[0158]

[0159] 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.

[0160] The contribution of hot electron excitation F el (V,T) is calculated by MermIn statistics:

[0161] F el (V,T)=E el (V,T)-TS el (V,T) (4)

[0162] Electron entropy S el Calculated by the following formula:

[0163] 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)

[0164] The hot electron energy is calculated by the following formula:

[0165]

[0166] where n(ε,V) is the electron density of states (e-DOS) of a single electron with energy ε, f is the Fermi function, ε F It's Fermi energy.

[0167] The modified Birch-Murnaghan equation of state (EOS) was then used to fit the Helmholtz energies at seven given volumes and temperatures:

[0168] F(V,T)=a+bV -2 / 3 +cV -4 / 3 +dV -2 +eV -8 / 3 (7)

[0169] Where a, b, c, d and e are fitting parameters, and 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:

[0170]

[0171] Calculated equilibrium volume V eq (T), the volume thermal expansion coefficient (β(T)) is calculated by the following formula:

[0172]

[0173] The relationship between the average linear expansion coefficients α(T) and β(T) is α(T)=β(T) / 3.

[0174] Adiabatic modulus B T (V,T) is calculated by the following formula:

[0175]

[0176] The main input data for thermodynamic modeling, entropy, can be derived as:

[0177]

[0178] Temperature dependence of enthalpy (H(V eq ,T)) can be calculated by the following formula:

[0179] H(V eq ,T)=U(V eq ,T)=F(V eq ,T)+TS(V eq ,T) (12)

[0180] Where U(V eq ,T) is the internal energy, which is the same as the isochoric melting (C V (V eq ,T)) has the following relationship:

[0181]

[0182] The isobaric heat capacity can be obtained from the following formula (14):

[0183] C P (V eq ,T)=C V (V eq ,T)+V eq TB T (V eq ,T)(β(T)) 2 (14)

[0184] Step 6: Based on the above calculations of the thermal properties of the Sn-In binary crystal structure, the In-Sb binary crystal structure, and the Sn-Sb binary crystal structure, and combined with the CALPHAD model, a thermodynamic model of the Sn-In-Sb system is established.

[0185] The CALPHAD model is described as follows:

[0186] The Gibbs energy of a compound at different temperatures is shown below:

[0187]

[0188] where a, b, c, d, e and f are model parameters evaluated from the thermodynamic data obtained from the first-principles quasi-harmonic calculations described above, H 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:

[0189]

[0190] where y i is the mole fraction of component i in the liquid phase, xs G Lis the excess Gibbs energy phase, represents the Gibbs energy of the pure liquid phase.

[0191] Excess Gibbs Energy xs G L The form is:

[0192]

[0193] in is the vth-order interaction parameter between components i and j and 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 model is used to thermodynamically optimize and calculate the Sn-In-Sb system phase diagram. The trial-and-error method is used to assign values ​​and optimize the calculation according to the thermodynamic data until it is basically consistent with the phase diagram and thermodynamic data. The liquid phase projection surface of the Sn-In-Sb system is obtained, such as Figure 7 As shown. According to the liquid phase projection surface of the Sn-In-Sb system, it is judged whether there is a eutectic point and the temperature range of the eutectic point in the Sn-In-Sb system. The results show that the Sn-In-Sb system has no eutectic point, so the structure is discarded.

[0197] The above-mentioned embodiment method 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 calculation combined with the CALPHAD model. The ternary alloy with a low eutectic point composition is screened out, and the error range is very small through experimental verification. This method selects ternary alloys that meet the requirements for experimental verification through theoretical calculation, which can save experimental time and resources, improve the efficiency of the experiment, play a guiding role, and avoid blindness.

[0198] The above is an explanation of the method embodiments of the present invention in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made according to the purpose of the invention of the present invention. Any parameter changes or calculation simplifications made according to the principle of the technical solution of the present invention, as long as they meet the purpose of the invention of the present invention and do not deviate from the principle and concept of the method for screening ultra-low melting point eutectic alloy welding materials based on the first principles of the present invention, belong to the protection scope of the present invention.

Claims

1. A method for screening ultra-low melting point eutectic alloy welding materials based on first principles, characterized in that: Includes the following: Step 1, obtaining a binary crystal structure existing in a Sn-In-TM system, wherein TM represents one of Sb, Ag, Zn, Bi, and Cu; Step 2, respectively conduct convergence tests on the cutoff energy and the k-point mesh density, select the cutoff energy corresponding to the lowest energy point, and select the k-point mesh density corresponding to the lowest energy point; Step 3: Based on the first principle calculation method of density functional theory, low-precision structural optimization is performed on each binary crystal structure, and the energy convergence criterion is 10 -6 eV, the force convergence criterion is Then, each binary crystal structure after low-precision optimization is subjected to high-precision structural optimization, and the energy convergence criterion is 10 -8 eV, the force convergence criterion is After reaching the convergence standard, the basic phase information is calculated based on each binary crystal structure after high-precision optimization; Step 4, based on each binary crystal structure after high-precision optimization, calculating the phonon spectrum of each binary crystal structure, and screening the binary crystal structure whose phonon spectrum has no imaginary frequency; Step 5, based on the quasi-harmonic approximation method, the thermal properties of each binary crystal structure with no imaginary frequency in the screened phonon spectrum are calculated respectively; Step 6, based on the calculated thermal properties of each binary crystal structure, thermodynamic data is obtained, and the CALPHAD model is combined to optimize the CALPHAD model parameters according to the thermodynamic data to establish a thermodynamic model of the Sn-In-TM system; Step 7, based on the thermodynamic model of the Sn-In-TM system, obtain the liquid phase projection surface of the Sn-In-TM system, analyze the composition ratio and temperature of the eutectic point, and screen out the ultra-low melting point eutectic alloy welding material.

2. The method for screening ultra-low melting point eutectic alloy welding materials based on first principles according to claim 1, characterized in that: Step 2 specifically includes: when testing the cutoff energy, select a k-point grid density of 4*4*4, fix other parameters, test the energies corresponding to different cutoff energies of 150, 200, 250, 300, 350, 400, 450, and 500 respectively, and select the truncation energy of 450 corresponding to the lowest energy point; then test the k-point grid density, select the truncation energy of 450, fix other parameters, test the energies under different k-point grid densities of 4*4*4, 6*6*6, 8*8*8, and 10*10*10 respectively, and select the k-point grid density of 8*8*8 corresponding to the lowest energy point.

3. The method for screening ultra-low melting point eutectic alloy welding materials based on first principles according to claim 1, characterized in that: Step 3 specifically includes: Step 3.1, set the parameter optimization parameters "ISIF = 3, IBRION = 2", perform low-precision structural optimization on the Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure respectively, and the energy convergence criterion is 10 -6 eV, the force convergence criterion is Step 3.2: After the low-precision structure optimization is completed, the high-precision structure optimization is performed again based on the Sn-In binary crystal structure, In-Bi binary crystal structure and Sn-Bi binary crystal structure after the low-precision structure optimization. The energy convergence criterion is 10 - 8 eV, the force convergence criterion is After two structural optimizations, the convergence standard was not reached. The optimization parameters were modified to "ISIF=2, IBRION=1" and the optimization was continued until the convergence standard was reached. Step 3.3, based on the structural energy after high-precision structural optimization, respectively calculate the basic phase information, the basic phase information includes formation enthalpy, and use the formation enthalpy calculation formula to respectively calculate the formation enthalpy of each binary crystal structure.

4. The method for screening ultra-low melting point eutectic alloy welding materials based on first principles according to claim 1, characterized in that: Step 4 specifically includes: Step 4.1, set the parameters "ISIF = 2, IBRION = 8", use the Phonopy finite displacement method to calculate the phonon spectrum of each binary crystal structure one by one, and there are imaginary frequencies at the high symmetry points of the phonon spectrum; Step 4.2, after high-precision structural optimization, the binary crystal structures are optimized again, and the force convergence criterion is raised to The energy convergence criterion remains unchanged, and each binary crystal structure is expanded by 2*2*2. The corresponding high symmetry k-point setting is reduced by half, and the phonon spectrum calculation is performed again until the phonon spectrum has no imaginary frequency.

5. The method for screening ultra-low melting point eutectic alloy welding materials based on first principles according to claim 1, characterized in that: The step 6 comprises: 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 the thermodynamic data obtained from the first-principles quasi-harmonic calculations described above, H SER The enthalpy of the most stable element at 298.15K and 1 bar is used as the reference state.

6. The method for screening ultra-low melting point eutectic alloy welding materials based on first principles according to claim 5, characterized in that: Step 6 further comprises: The Gibbs energy of the liquid phase is expressed as: 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 and is given by: Model parameters v,Liq A and v,Liq B is estimated from thermodynamic data and liquid-related phase boundary data.

7. The method for screening ultra-low melting point eutectic alloy welding materials based on first principles according to claim 6, characterized in that: The thermodynamic model of the Sn-In-Bi system is:

8. The method for screening ultra-low melting point eutectic alloy welding materials based on first principles according to any one of claims 1 to 7, characterized in that: The composition ratio of Sn:In:Bi screened from the Sn-In-Bi system is (18.15-22.76):(30.57-33.54):(41.58-45.31), and the eutectic temperature is 41.6-45.7°C.

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