A method for splitting semi-coherent two-phase diffraction curves

Abstract

The present disclosure discloses a method for splitting a semi-coherent two-phase diffraction curve, comprising: obtaining a relative volume fraction V of the semi-coherent two-phase a and b in the metal material by characterizing the microstructure of the metal material. a and V b , and V a +V b =1; calculate the diffraction structure factor F of phase a and phase b respectively a and F b ; Obtain the diffraction vector modulus length-diffraction intensity curve xq-yi of phase a and phase b by diffraction; Fit the diffraction vector modulus length-diffraction intensity curve xq-yi to obtain the diffraction vector modulus length-diffraction intensity fitting curve XQ-YI; Split the diffraction vector modulus length-diffraction intensity fitting curve XQ-YI according to the mirror rule to obtain several groups of diffraction curves; According to the relative volume fraction V of phase a and phase b a and V b and the diffraction structure factor F a and F b , select the diffraction curves of phase a and phase b from several groups of diffraction curves.

Description

Technical Field

[0001] The present invention belongs to the field of diffraction technology, and in particular relates to a method for splitting semi-coherent two-phase diffraction curves. Background Art

[0002] Semi-coherent two-phase structural materials usually exhibit excellent physical and mechanical properties. In order to meet specific service conditions, the engineering field often designs two-phase structural materials with semi-coherent crystallographic relationships. At the same time, the characteristics of semi-coherence also determine that the mismatch between the two phases of the material is extremely small. Taking the third-generation precipitation-strengthened nickel-based high-temperature alloy as an example, the mismatch at room temperature is generally less than one percent. The performance is determined by the structure. In order to continuously optimize the various aspects of the performance of semi-coherent structural materials, the fine characterization of its microstructure is essential. The commonly used means are diffraction techniques, such as X-ray diffraction technology, neutron diffraction technology, etc. The difficulty is that the mismatch between the two phases of the semi-coherent is extremely small, resulting in a high degree of overlap between the diffraction curves of the two phases, which cannot be directly distinguished. This is a great challenge for fine characterization.

[0003] The existing curve splitting method is based on the asymmetry of the diffraction curve on both sides of the intensity peak to obtain the diffraction curves of the two semi-coherent phases. This method provides the most basic splitting idea and has reference significance, but it also has great limitations. The method only considers the asymmetry of the diffraction curve, and does not consider the volume fraction of the two semi-coherent phases in the structural material and the diffraction structure factor (the volume fraction and the diffraction structure factor will directly affect the ratio of the diffraction intensity integrals of the two semi-coherent phases, that is, the ratio of the integral area of ​​the diffraction curve). Therefore, it will inevitably lead to the diffraction curve obtained by this method that cannot reasonably and truly reflect the intrinsic structural characteristics of the two-phase material, which runs counter to the original intention of fine characterization and may even mislead the design of the structure. Therefore, it is urgent to develop a novel and more reasonable curve splitting method to deal with the diffraction curves of semi-coherent two-phase structural materials. Summary of the invention

[0004] In view of the deficiencies in the prior art, the purpose of the present invention is to provide a method for splitting the diffraction curves of semi-coherent two phases. The method comprehensively considers the relative volume fractions of the semi-coherent two phases and the diffraction structure factor. Compared with the method of splitting the diffraction curves of the semi-coherent two phases only relying on the curve characteristics, the diffraction curves of the semi-coherent two phases obtained by the method can reasonably and truly reflect the intrinsic characteristics of the two-phase material.

[0005] To achieve the above objectives, the present disclosure provides the following technical solutions:

[0006] A method for splitting a semi-coherent two-phase diffraction curve comprises the following steps:

[0007] S100: By characterizing the microstructure of metal materials, the relative volume fraction V of the semi-coherent two phases a and b in the metal materials is obtained. a and V b , and V a +V b =1;

[0008] S200: Calculate the diffraction structure factor F of phase a and phase b respectively a and F b ;

[0009] S300: obtaining the diffraction vector mode length-diffraction intensity curve xq-yi of phase a and phase b by diffraction;

[0010] S400: fitting the diffraction vector modulus length-diffraction intensity curve xq-yi to obtain a diffraction vector modulus length-diffraction intensity fitting curve XQ-YI;

[0011] S500: splitting the diffraction vector modulus-diffraction intensity fitting curve XQ-YI according to the mirror rule to obtain a plurality of groups of diffraction curves;

[0012] S600: According to the relative volume fraction V of phase a and phase b a and V b and the diffraction structure factor F a and F b , select the diffraction curves of phase a and phase b from several groups of diffraction curves.

[0013] Preferably, in step S200, the diffraction structure factor F a Calculated by the following formula:

[0014]

[0015] The diffraction structure factor F b Calculated by the following formula:

[0016]

[0017] Where n is the different positions occupied by the basic unit, n = 1, 2, ..., N, N is the total number of positions occupied by the basic unit constituting the unit cell; π is the circumference of a circle; i is the symbol for an imaginary number in mathematics; hkl is the Miller index, indicating that the crystal plane where diffraction occurs is (hkl), and the value ranges of h, k, and l are all integers in the interval [0, ∞); u n 、v n 、w n are the horizontal, vertical and vertical coordinates of the position n occupied by the basic unit, and u n 、v n 、w nThe value range of f is a real number in the interval [0, 1]; n is the scattering factor of the basic unit.

[0018] Preferably, the scattering factor f n Calculated by the following formula:

[0019]

[0020] Wherein, m is the smallest unit constituting different positions n, and m=1, 2, ..., M, M is the number of the smallest units; f n，m is the scattering factor of the smallest unit m; is the probability of the smallest unit m appearing in different positions n, and satisfies the relationship

[0021] Preferably, step S500 includes the following steps:

[0022] S501: The horizontal coordinates of all the values ​​in the diffraction vector modulus-diffraction intensity fitting curve XQ-YI are used to form a one-dimensional arithmetic vector XQ, and the difference between adjacent elements of XQ is recorded as ΔXQ;

[0023] S502: The horizontal coordinate XQ of the peak value of the diffraction vector modulus length-diffraction intensity fitting curve XQ-YI is calculated. max With L as the radius and centered at , a one-dimensional arithmetic vector XQL with 2L+1 elements is generated. The difference between adjacent elements of XQL is equal to ΔXQ.

[0024] S503: On the diffraction vector modulus length-diffraction intensity fitting curve XQ-YI, take the lth element XQ of the vector XQL l is the data point corresponding to the horizontal axis (XQ l , YI l ) and (XQ l , 0) is a mirror surface, and the diffraction vector modulus-diffraction intensity fitting curve XQ-YI is located at (XQ l , YI l ) The right part is mirrored and symmetrically operated to obtain the primary symmetric curve XQ l_RR -YI l_RR ;

[0025] S504: Subtract the primary symmetry curve XQ from the diffraction vector modulus-diffraction intensity fitting curve XQ-YI l_RR -YI l_RR , that is, the initial difference curve XQ is obtained l_R- -YI l_R- ;

[0026] S505: Using the initial difference curve XQ l_R- -YIl_R -The peak value and the line segment where the peak value is projected on the XQ axis are mirror surfaces. l_R- -YI l_R -The part on the left side of the peak is mirrored to obtain the quadratic symmetric curve XQ l_LL -YI l_LL ;

[0027] S506: Subtract the quadratic symmetry curve XQ from the diffraction vector modulus-diffraction intensity fitting curve XQ-YI l_LL -YI l_LL , that is, the quadratic difference curve XQ is obtained l_L- -YI l_L- , quadratic symmetry curve XQ l_LL -YI l_LL and the quadratic difference curve XQ l_L- -YI l_L - is the first group of diffraction curves of the diffraction vector mode length-diffraction intensity fitting curve XQ-YI;

[0028] S507: Repeat steps S503 to S506 for the 2L+1 elements in the one-dimensional arithmetic vector XQL, that is, perform 2L+1 splits on the diffraction vector modulus length-diffraction intensity fitting curve XQ-YI, that is, obtain 2L+1 sets of quadratic symmetric curves XQ l_LL -YI l_LL and the quadratic difference curve XQ l_L- -YI l_L- .

[0029] Preferably, step S600 includes the following steps:

[0030] S601: For 2L+1 groups of quadratic symmetric curves XQ l_LL -YI l_LL Perform the integral operation to obtain 2L+1 group of integral results, recorded as ITG l_LL ; For the 2L+1 group of quadratic difference curves XQ l_L- -YI l_L - Perform integration operation to obtain 2L+1 group of integration results, recorded as ITG l_L- ;

[0031] S602: According to ITG l_LL and ITG l_L- Calculate the deviation value δ of 2L+1 group l ;

[0032] S603: Select 2L+1 groups of deviation values ​​δ l The minimum value in l′ , then δ l′ The corresponding quadratic symmetry curve XQl′_LL -YI l′_LL and the quadratic asymmetric curve XQ l′_L- -YI l′_L - are the diffraction curves of phase a and phase b, respectively denoted as XQ a -YI a and XQ b -YI b .

[0033] Preferably, in step S602, the deviation value δ is calculated by the following formula: l :

[0034]

[0035] Among them, V a and V b are the relative volume fractions of phase a and phase b, F a and F b are the diffraction structure factors of phase a and phase b, respectively.

[0036] Preferably, in step S400, any function including a polynomial function P(x), a Gauss function G(x), a Lorentz function L(x) and a Voigt function V(x) is used to fit the diffraction vector modulus length-diffraction intensity curve xq-yi, wherein:

[0037] The polynomial function P(x) is expressed as:

[0038] P(x)=a n x n +a n-1 x n-1 +…+a2x 2 +a1x+a0

[0039] The Gauss function G(x) is expressed as:

[0040]

[0041] The Lorentz function L(x) is expressed as:

[0042]

[0043] The Voigt function V(x) is expressed as:

[0044]

[0045] Among them, a0, a1, a2, a n-1 , a n, A, B, C, A′, B′, C′, σ, γ are the coefficients of the function, e is a natural number, and π is the ratio of a circle to a circle.

[0046] Preferably, the present disclosure further provides a computer, comprising:

[0047] Memory, for storing computer instructions;

[0048] A processor is used to execute computer instructions to implement any of the above methods.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] 1. Before implementing curve splitting, the diffraction vector mode length-diffraction intensity curve of the semi-coherent two-phase is fitted to obtain a diffraction vector mode length-diffraction intensity fitting curve with infinite resolution in principle, which can improve the accuracy of curve splitting;

[0051] 2. By comprehensively considering the relative volume fractions of the semi-coherent two phases and the diffraction structure factor, the intrinsic characteristics of the two-phase material can be reasonably and truly reflected, thus overcoming the shortcomings of splitting solely based on curve characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a flow chart of a method for splitting a semi-coherent two-phase diffraction curve provided by an embodiment of the present disclosure;

[0053] Figure 2 is a schematic diagram of the morphology characterization of semi-coherent two phases a and b of a nickel-based high-temperature alloy obtained by scanning electron microscope observation according to another embodiment of the present disclosure;

[0054] Figure 3 is a diffraction vector mode length-diffraction intensity curve xq-yi of semi-coherent two phases a and b of a nickel-based high-temperature alloy obtained by X-ray diffraction provided by another embodiment of the present disclosure;

[0055] Figure 4 A diffraction vector modulus length-diffraction intensity fitting curve XQ-YI is obtained by fitting the curve xq-yi using a Gauss function provided in another embodiment of the present disclosure;

[0056] FIG. 5( a ) and FIG. 5( b ) are diffraction curves obtained by splitting the diffraction vector modulus-diffraction intensity fitting curve XQ-YI according to the mirror rule provided in another embodiment of the present disclosure, wherein FIG. 5( a ) corresponds to l=1201, and FIG. 5( b ) corresponds to l=2001;

[0057] Figure 6 is a quadratic symmetric curve XQ provided by another embodiment of the present disclosure l_LL -YIl_LL The corresponding integral value ITG l_LL And the quadratic difference curve XQ l_L- -YI l_L- The corresponding integral value ITG l_L- Schematic diagram of the results;

[0058] Figure 7 is a result schematic diagram of a deviation value δl provided by another embodiment of the present disclosure;

[0059] Figure 8 is the primary symmetry curve XQ provided by another embodiment of the present disclosure 1417_RR -YI 1417_RR and the initial difference curve XQ 1417_R- -YI 1417_R- Schematic diagram of the results;

[0060] Fig. 9 is a diffraction curve XQ of the semi-coherent two-phase a and b of a nickel-based high-temperature alloy provided by another embodiment of the present disclosure a -YI a and XQ b -YI b ;

[0061] Fig.10 Another embodiment of the present disclosure provides a diffraction curve of semi-coherent two phases a and b of a nickel-based high-temperature alloy obtained by splitting the curve using the asymmetry of the diffraction peak. DETAILED DESCRIPTION

[0062] The following will refer to the attached Figures 1 to 10 Specific embodiments of the present disclosure are described in detail. Although specific embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0063] It should be noted that certain words are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different nouns to refer to the same component. This specification and claims do not use the difference in nouns as a way to distinguish components, but use the difference in the functions of the components as the criterion for distinction. As mentioned throughout the specification and claims, "including" or "comprising" is an open term, so it should be interpreted as "including but not limited to". The subsequent description of the specification is a preferred embodiment of the present disclosure, but the description is based on the general principles of the specification and is not used to limit the scope of the present disclosure. The scope of protection of the present disclosure shall be determined by the attached claims.

[0064] To facilitate understanding of the embodiments of the present disclosure, further explanation will be given below using specific embodiments as examples in conjunction with the accompanying drawings, and each of the accompanying drawings does not constitute a limitation on the embodiments of the present disclosure.

[0065] In one embodiment, if Figure 1 As shown, the present disclosure provides a method for splitting a semi-coherent two-phase diffraction curve, comprising the following steps:

[0066] S100: By characterizing the microstructure of metal materials, the relative volume fraction V of the semi-coherent two phases a and b in the metal materials is obtained. a and V b , and V a +V b =1;

[0067] S200: Calculate the diffraction structure factor F of phase a and phase b respectively a and F b ;

[0068] S300: obtaining the diffraction vector mode length-diffraction intensity curve xq-yi of phase a and phase b by diffraction;

[0069] S400: fitting the diffraction vector modulus length-diffraction intensity curve xq-yi to obtain a diffraction vector modulus length-diffraction intensity fitting curve XQ-YI;

[0070] S500: splitting the diffraction vector modulus-diffraction intensity fitting curve XQ-YI according to the mirror rule to obtain a plurality of groups of diffraction curves;

[0071] S600: According to the relative volume fraction V of phase a and phase b a and V b and the diffraction structure factor F a and F b , select the diffraction curves of phase a and phase b from several groups of diffraction curves.

[0072] In this embodiment, before the curve is split, the diffraction vector modulus length-diffraction intensity curve of the semi-coherent two-phase is first fitted to obtain the diffraction vector modulus length-diffraction intensity fitting curve, so as to improve the accuracy of the curve splitting. Because in the process of diffraction experiment, in order to achieve the subjective purpose of saving time, or due to objective factors limited by experimental conditions, the resolution of the collected diffraction data is often insufficient, which affects the accuracy of the final curve splitting. Therefore, the experimental data point, i.e., the diffraction vector modulus length-diffraction intensity curve, is first fitted by a suitable mathematical function to obtain a diffraction vector modulus length-diffraction intensity fitting curve with infinite resolution in principle, and then the curve is split, which ultimately greatly improves the accuracy of the curve splitting. In addition, when determining the diffraction curve of the semi-coherent two-phase, the relative volume fraction and diffraction structure factor of the semi-coherent two-phase are comprehensively considered in this embodiment, and the microstructure, crystal structure and composition of the two-phase are fully utilized, so that the diffraction curve of the semi-coherent two-phase obtained can reasonably and truly reflect the intrinsic characteristics of the dual-phase material, thereby achieving the purpose of fine characterization and guiding material design.

[0073] In another embodiment, in step S200, the diffraction structure factor F a Calculated by the following formula:

[0074]

[0075] The diffraction structure factor F b Calculated by the following formula:

[0076]

[0077] Where n is the different positions occupied by the basic unit, n = 1, 2, ..., N, N is the total number of positions occupied by the basic unit constituting the unit cell; π is the circumference of a circle; i is the symbol for an imaginary number in mathematics; hkl is the Miller index, representing that the crystal plane where diffraction occurs is (hkl), and the value ranges of h, k, and l are all integers in the interval [0, ∞); u n 、v n 、w n are the horizontal, vertical and vertical coordinates of the position n occupied by the basic unit, and u n 、v n 、w n The value range of f is a real number in the interval [0, 1]; n is the scattering factor of the basic unit.

[0078] In another embodiment, the scattering factor f n Calculated by the following formula:

[0079]

[0080] Wherein, m is the smallest unit constituting different positions n, and m=1, 2, ..., M, M is the number of the smallest units; f n，m is the scattering factor of the smallest unit m; is the probability of the smallest unit m appearing in different positions n, and satisfies the relationship

[0081] In another embodiment, step S500 includes the following steps:

[0082] S501: The horizontal coordinates of all the values ​​in the diffraction vector modulus-diffraction intensity fitting curve XQ-YI are used to form a one-dimensional arithmetic vector XQ, and the difference between adjacent elements of XQ is recorded as ΔXQ;

[0083] S502: The horizontal coordinate XQ of the peak value of the diffraction vector modulus length-diffraction intensity fitting curve XQ-YI is calculated. max With L as the radius and centered at , a one-dimensional arithmetic vector XQL with 2L+1 elements is generated. The difference between adjacent elements of XQL is equal to ΔXQ.

[0084] S503: On the diffraction vector modulus length-diffraction intensity fitting curve XQ-YI, take the lth element XQ of the vector XQL l is the data point corresponding to the horizontal axis (XQ l , YI l ) and (XQ l , 0) is a mirror surface, and the diffraction vector modulus-diffraction intensity fitting curve XQ-YI is located at (XQ l , YI l ) The right part is mirrored and symmetrically operated to obtain the primary symmetric curve XQ l_RR -YI l_RR ;

[0085] S504: Subtract the primary symmetry curve XQ from the diffraction vector modulus-diffraction intensity fitting curve XQ-YI l_RR -YI l_RR , to obtain the initial difference curve XQ l_R- -YI l_R- ;

[0086] S505: Using the initial difference curve XQ l_R- -YI l_R- The peak value and the line segment where the peak value is projected on the XQ axis are mirror surfaces. l_R- -YI l_R- The part on the left side of the peak is mirrored to obtain the quadratic symmetric curve XQ l_LL -YI l_LL ;

[0087] S506: Subtract the quadratic symmetry curve XQ from the diffraction vector modulus-diffraction intensity fitting curve XQ-YI l_LL -YI l_LL , to obtain the quadratic difference curve XQ l_L- -YI l_L- , quadratic symmetry curve XQ l_LL -YI l_LL and the quadratic difference curve XQ l_L- -YI l_L- That is, the first group of diffraction curves of the diffraction vector mode length-diffraction intensity fitting curve XQ-YI;

[0088] S507: Repeat steps S503 to S506 for the 2L+1 elements in the one-dimensional arithmetic vector XQL, that is, perform 2L+1 splits on the diffraction vector modulus length-diffraction intensity fitting curve XQ-YI, that is, obtain 2L+1 sets of quadratic symmetric curves XQ l_LL -YI l_LL and the quadratic difference curve XQ l_L- -YI l_L- .

[0089] In another embodiment, step S600 includes the following steps:

[0090] S601: For 2L+1 groups of quadratic symmetric curves XQ l_LL -YI l_LL Perform the integral operation to obtain 2L+1 group of integral results, recorded as ITG l_LL ; For the 2L+1 group of quadratic difference curves XQ l_L- -YI l_L- Perform the integral operation to obtain 2L+1 group of integral results, recorded as ITG l_L- ;

[0091] S602: According to ITG l_LL and ITG l_L- Calculate the deviation value δ of 2L+1 group l , the deviation value δ l Calculated by the following formula:

[0092]

[0093] Among them, V a and V b are the relative volume fractions of the semi-coherent two phases a and b, F a and F b are the diffraction structure factors of the semi-coherent phases a and b respectively.

[0094] S603: Select 2L+1 groups of deviation values ​​δ l The minimum value in l′, the subscript l′ is an integer in the interval [1, 2L+1], then δ l′ The corresponding quadratic symmetry curve XQ l′_LL -YI l′_LL and the quadratic asymmetric curve XQ l′_L- -YI l′_L- These are the diffraction curves of phase a and phase b, denoted as XQ a -YI a and XQ b -YI b .

[0095] Below, the technical solution of the present disclosure is described in detail by taking X-ray diffraction of nickel-based high-temperature alloy as an example.

[0096] 1. For the microstructure of nickel-based high-temperature alloy, the scanning electron microscope is used to obtain the following Figure 2 The morphology of phase a and phase b in the semi-coherent two phases is shown in FIG. 1 . By observing the relative volume fractions of phase a and phase b in the semi-coherent two phases, the relative volume fractions of phase a and phase b are respectively: V a =30%, V b =70%, and V a +V b =30%+70%=1.

[0097] 2. Calculate the diffraction structure factor F of phase a and phase b respectively a and F b ,in,

[0098] The diffraction structure factor F of the a phase a The calculation formula is:

[0099]

[0100] In nickel-based high-temperature alloys, the a phase has a face-centered cubic crystal structure: the total number of positions occupied by the basic unit of the unit cell is 4, that is, N = 4; the coordinates of the position n occupied by the basic unit are (u n , v n , w n), when n=1, (u1, v1, w1)=(0, 0, 0), when n=2, (u2, v2, w2)=(0, 1 / 2, 1 / 2), when n=3, (u3, v3, w3)=(1 / 2, 0, 1 / 2), when n=4, (u4, v4, w4)=(1 / 2, 1 / 2, 0); the crystal plane index (hkl) where diffraction occurs is (800), that is, h=8, k=0, l=0, where hkl is the Miller index, indicating that the crystal plane where diffraction occurs is (hkl), and the value ranges of h, k, and l are all integers in the interval [0, ∞); f1, f2, f3, and f4 are the scattering factors f of the basic units occupying the four positions of n=1, n=2, n=3, and n=4 respectively. n , f n The calculation formula is expressed as:

[0101]

[0102] In nickel-based high-temperature alloys, the f n Satisfies f1=f2=f3=f4. The basic unit occupying position n is composed of a total of three minimum units, namely, M=3; the minimum unit of m=1 is Ni atom, f n，1 =f Ni =28.3372+0.7725i, the smallest unit with m=2 is Co atom, f n，2 =f Co =27.3187+0.6608i, the smallest unit of m=3 is Cr atom, f n，3 =f Cr =24.2626+0.4175i; is the probability of the smallest unit m appearing at position n, f Ni , f Co , f Cr They are the scattering factor of Ni atoms, the scattering factor of Co atoms, and the scattering factor of Cr atoms respectively.

[0103] Substitute the above variables into the calculation formula of the diffraction structure factor of the a phase in the nickel-based high-temperature alloy:

[0104]

[0105] Finally got F a =107.69+2.57i.

[0106] Similarly, the diffraction structure factor F of the b phase b The calculation formula is:

[0107]

[0108] In nickel-based high-temperature alloys, the b phase has an L12 crystal structure: the total number of positions occupied by the basic unit of the unit cell is 4, that is, N = 4; the coordinates of the position n occupied by the basic unit (u n , v n , w n ), when n=1, (u1, v1, w1)=(0, 0, 0), when n=2, (u2, v2, w2)=(0, 1 / 2, 1 / 2), when n=3, (u3, v3, w3)=(1 / 2, 0, 1 / 2), when n=4, (u4, v4, w4)=(1 / 2, 1 / 2, 0); the crystal plane index (hkl) where diffraction occurs is (800); f1, f2, f3, f4 are the scattering factors f of the basic units occupying the four positions of n=1, n=2, n=3, n=4 respectively n , f n The calculation formula is:

[0109]

[0110] In nickel-based high-temperature alloys, the f n Satisfies f1≠f2=f3=f4. The basic unit occupying position n=1 is composed of two minimum units in total, that is, M=2, and the basic units occupying positions n=2, 3, and 4 are composed of only one minimum unit; when n=1, m=1, the minimum unit is Al atom, f 1，1 =f Al =13.0435+0.0337i, when n=1, m=2, the smallest unit is Ti atom, f 1，2 =f Ti =22.2247+0.3060i, when n=2, 3, 4, the smallest unit occupying position n is Ni atom, f2=f3=f4=f Ni =28.3372+0.7725i; is the probability of the smallest unit m appearing at position n, f Al is the scattering factor of Al atoms, f Ti is the scattering factor of Ti atoms.

[0111] Substitute the above variables into the calculation formula of the diffraction structure factor of the b phase in the nickel-based high-temperature alloy:

[0112]

[0113] Finally got F b =100.99+2.44i.

[0114] 3. Obtain the following by any X-ray diffraction method including but not limited to X-ray diffraction, neutron diffraction and electron diffraction: Figure 3The diffraction vector mode length-diffraction intensity curve xq-yi of phase a and phase b on the crystal plane (800) is shown, where the horizontal coordinate range of the curve xq-yi is [139.51, 141.31], the accuracy is 0.03, and the unit is nm -1 .

[0115] 4. Use any function including polynomial function P(x), Gauss function G(x), Lorentz function L(x) and Voigt function V(x) to fit the diffraction vector mode length-diffraction intensity curve xq-yi to obtain Figure 4 The diffraction vector mode length-diffraction intensity fitting curve XQ-YI is shown, where

[0116] The polynomial function P (red) is expressed as:

[0117] P(x)=a n x n +a n-1 x n-1 +...+a2x 2 +a1x+a0

[0118] The Gauss function G(x) is expressed as:

[0119]

[0120] The Lorentz function L(x) is expressed as:

[0121]

[0122] The Voigt function V(x) is expressed as:

[0123]

[0124] Among them, a0, a1, a2, a n-1 , a n , A, B, C, A′, B′, C′, σ, γ are the coefficients of the function, e is a natural number, and π is the ratio of a circle to a circle.

[0125] Next, the Gauss function G(x) is used as an example to fit the diffraction vector mode length-diffraction intensity curve xq-yi:

[0126]

[0127] In the above formula, A, B, and C are unknown coefficients. Taking the natural logarithm on both sides of the equation, we get:

[0128]

[0129] All data points (x j ,y j ) into the above equation, we get:

[0130]

[0131] According to the generalized least squares solution, the coefficients A, B, C are obtained, and the expression of the function G(x) is determined. Wherein, s is the total number of all data points on the diffraction vector modulus-diffraction intensity curve xq-yi, and j is an integer in the interval [1, s].

[0132] 5. Split the diffraction vector modulus-diffraction intensity fitting curve XQ-YI according to the mirror rule. The specific steps are as follows:

[0133] 5.1. The horizontal coordinates of all the values ​​in the diffraction vector modulus-diffraction intensity fitting curve XQ-YI form a one-dimensional arithmetic vector XQ, XQ = [139.5100: 0.0001: 141.3100], the difference between adjacent elements of vector XQ ΔXQ = 0.0001 (ΔXQ = 0.0001 is an artificially specified step size), the unit is nm -1 ;

[0134] 5.2. The horizontal coordinate XQ of the peak value of the diffraction vector mode length-diffraction intensity fitting curve XQ-YI is max =140.4033nm -1 With L=1000 as the radius (L is an artificially defined range, which means taking the peak value of the curve as the reference, taking L data points to the left and L data points to the right, so L is called the radius, and the value range of L is less than a positive integer of half the length of XQ), a one-dimensional arithmetic vector XQL with 2L+1=2001 elements is generated, and the difference between adjacent elements of vector XQL is equal to ΔXQ=0.0001nm -1 , that is, the lth element of vector XQL XQL(l) = XQ max -(l-1-L)×ΔXQ=140.4033-(l-1001)×0.0001, l is an integer in the interval [1, 2001], XQL=[140.3033:0.0001:140.5033], the unit is nm -1 ;

[0135] 5.3. On the diffraction vector modulus length-diffraction intensity fitting curve XQ-YI, the lth element XQ of the vector XQL l is the data point corresponding to the horizontal axis (XQ l , YI l ) and (XQ l, 0) is a mirror surface, and the diffraction vector modulus-diffraction intensity fitting curve XQ-YI is located at (XQ l , YI l ) The right part is mirrored and symmetrically operated to obtain the primary symmetric curve XQ l_RR -YI l_ RR;

[0136] 5.4. Subtract the primary symmetry curve XQ from the diffraction vector mode length-diffraction intensity fitting curve XQ-YI l_RR -YI l_RR , that is, the initial difference curve XQ is obtained l_R- -YI l_R- ;

[0137] 5.5. Using the initial difference curve XQ l_R- -YI l_R -The peak value and the line segment where the peak value is projected on the XQ axis are mirror surfaces. l_R- -YI l_R- The part on the left side of the peak is mirrored and symmetrically operated to obtain the quadratic symmetrical curve XQ l_LL -YI l_LL ;

[0138] 5.6. Subtract the quadratic symmetry curve XQ from the diffraction vector modulus-diffraction intensity fitting curve XQ-YI l_LL -YI l_LL , that is, the quadratic difference curve XQ is obtained l_L- -YI l_L- , quadratic symmetry curve XQ l_LL -YI l_LL and the quadratic difference curve XQ l_L- -YI l_L- That is, the first group of diffraction curves of the diffraction vector mode length-diffraction intensity fitting curve XQ-YI;

[0139] 5.7. Repeat the operations from step 5.3 to step 5.6 for the 2L+1=2001 elements in the one-dimensional arithmetic vector XQL, that is, perform 2L+1=2001 splits on the diffraction vector modulus-diffraction intensity fitting curve XQ-YI, that is, obtain 2L+1=2001 groups of diffraction curves. The operations from step 5.3 to step 5.6 are the mirror rule, such as Figure 5(a) and 5(b) Shown are the diffraction curves of l=1201 and l=2001 respectively.

[0140] 6. According to the relative volume fraction V of phase a and phase b a and V b and the diffraction structure factor F a and F b, select the diffraction curves of phase a and phase b from 2001 sets of diffraction curves. The specific steps are as follows:

[0141] 6.1. For 2L+1 groups of quadratic symmetric curves XQ l_LL -YI l_LL Perform the integral operation to obtain 2L+1 group of integral results, recorded as ITG l_LL ; For the 2L+1 group of quadratic difference curves XQ l_L- -YI l_L - Perform integration operation to obtain 2L+1 group of integration results, recorded as ITG l_L- Among them, ITG l_LL and ITG l_L- Some of the results are as follows Figure 6 shown.

[0142] 6.2 According to ITG l_LL and ITG l_L- Calculate the 2L+1 group deviation δ l , expressed as:

[0143]

[0144] Among them, V a and V b are the relative volume fractions of phase a and phase b, V a =30%, V b =70%, F a and F b are the diffraction structure factors of phase a and phase b, respectively, F a =107.69+2.57i-, F b =100.99+2.44i, substitute into the equation to calculate the deviation value δ l , δ l Some of the results are as follows Figure 7 shown.

[0145] It should be noted that the deviation value δ l The physical meaning is: the two curves XQ obtained by splitting l_LL -YI l_LL and XQ l_L- -YI l_L- The ratio of the integrated area The ratio of the integrated area of ​​the diffraction curves of the theoretical semi-coherent two phases a and b is The deviation between .

[0146] 6.3, 2L+1=2001 deviation values ​​δ l The minimum value of l′ , δ l′ =2.2×10 -4, subscript l′=1417, first symmetry curve XQ 1417_RR -YI 1417_RR and the initial difference curve XQ 1417_R- -YI 1417_R- like Figure 8 As shown, the first symmetry curve XQ 1417_RR -YI 1417_RR The right half of comes from the diffraction vector mode length-diffraction intensity fitting curve XQ-YI, and the left half is obtained by the mirror symmetry operation of the right half. 1417_R-- YI 1417_R- It is obtained by subtracting the diffraction vector modulus-diffraction intensity fitting curve XQ-YI from the primary symmetry curve. Then the secondary symmetry curve XQ 1417_LL -YI 1417_LL and the quadratic difference curve XQ 1417_L-- YI 1417_L- This is the selected diffraction curve, denoted as XQ a -YI a and XQ b -YI b , that is, Fig. 9 Diffraction curves of semi-coherent phases a and b are shown.

[0147] When the asymmetry of the diffraction curve on both sides of the intensity peak is used to split the diffraction vector mode length-diffraction intensity fitting curve XQ-YI, the diffraction curves of the a-phase and b-phase are obtained as shown in Fig.10 As shown in the figure, the ratio of the integrated area of ​​the diffraction curve of phase a to the integrated area of ​​the diffraction curve of phase b is 14.16%. Fig. 9 The a-phase diffraction curve, Fig.10 The integral area of ​​the a-phase diffraction curve is obviously lower than that of Fig. 9 The b-phase diffraction curve, Fig.10 The integral area of ​​the b-phase diffraction curve is obviously higher. Fig.10 The ratio of the integrated areas of the two diffraction curves obtained by splitting is 14.16%, which is obviously deviated from the theoretical value.

[0148] According to the results of the above embodiments, Fig. 9 As shown, the diffraction curve XQ of the a phase a -YI a The diffraction curve XQ of the b phase b -YI b The ratio of the integrated area of ​​the theoretical semi-coherent two-phase a and b diffraction curve is 48.71%. Obviously, when the curve is split according to the method provided in the present disclosure, the ratio of the integrated areas of the diffraction curves of the semi-coherent two phases a and b is closer to the theoretical value, and therefore can better reflect the intrinsic structural characteristics of the dual-phase material.

[0149] In another embodiment, the present disclosure further provides a computer, comprising:

[0150] Memory, for storing computer instructions;

[0151] A processor is used to execute computer instructions to implement any method of the aforementioned embodiments.

[0152] The technical solutions provided by the present disclosure are described in detail above in combination with specific embodiments. Meanwhile, the description of the above embodiments is only used to help understand the method and core idea of ​​the present disclosure. For those skilled in the art, according to the idea of ​​the present disclosure, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be understood as limiting the present disclosure.

Claims

1. A method for splitting a semi-coherent two-phase diffraction curve, comprising the following steps: S100: Obtain the relative volume fraction V of the semi-coherent two phases a and b in the metal material by characterizing the microstructure of the metal material a and V b , and V a +V b =1; S200: Calculate the diffraction structure factor F of phase a and phase b respectively a and F b ; S300: obtaining the diffraction vector mode length-diffraction intensity curve xq-yi of phase a and phase b by diffraction; S400: fitting the diffraction vector modulus length-diffraction intensity curve xq-yi to obtain a diffraction vector modulus length-diffraction intensity fitting curve XQ-YI; S500: splitting the diffraction vector modulus-diffraction intensity fitting curve XQ-YI according to the mirror rule to obtain a plurality of groups of diffraction curves; Step S500 includes the following steps: S501: The horizontal coordinates of all the values ​​in the diffraction vector modulus-diffraction intensity fitting curve XQ-YI are used to form a one-dimensional arithmetic vector XQ, and the difference between adjacent elements of XQ is recorded as ΔXQ; S502: The horizontal coordinate XQ of the peak value of the diffraction vector modulus length-diffraction intensity fitting curve XQ-YI is calculated. max With L as the radius and centered at , a one-dimensional arithmetic vector XQL with 2L+1 elements is generated, and the difference between adjacent elements of XQL is equal to ΔXQ; S503: On the diffraction vector modulus length-diffraction intensity fitting curve XQ-YI, take the lth element XQ of the vector XQL l is the data point corresponding to the horizontal axis (XQ l , YI l ) and (XQ l , 0) is a mirror surface, and the diffraction vector modulus length-diffraction intensity fitting curve XQ-YI is located at (XQ l , YI l ) The right part is mirrored and symmetrically operated to obtain the primary symmetric curve XQ l_RR -YI l_RR ; S504: Subtract the primary symmetry curve XQ from the diffraction vector modulus-diffraction intensity fitting curve XQ-YI l_RR -YI l_RR , that is, the initial difference curve XQ is obtained l_R- -YI l_R- ; S505: Using the initial difference curve XQ l_R- -YI l_R- The peak value and the line segment where the peak value is projected on the XQ axis are mirror surfaces. l_R- -YI l_R- The part on the left side of the peak is mirrored and symmetrically operated to obtain the quadratic symmetrical curve XQ l_LL -YI l_LL ; S506: Subtract the quadratic symmetry curve XQ from the diffraction vector modulus-diffraction intensity fitting curve XQ-YI l_LL -YI l_LL , that is, the quadratic difference curve XQ is obtained l_L- -YI l_L- , quadratic symmetry curve XQ l_LL -YI l_LL and the quadratic difference curve XQ l_L- -YI l_L- That is, the first group of diffraction curves of the diffraction vector mode length-diffraction intensity fitting curve XQ-YI; S507: Repeat steps S503 to S506 for the 2L+1 elements in the one-dimensional arithmetic vector XQL, that is, perform 2L+1 splits on the diffraction vector modulus length-diffraction intensity fitting curve XQ-YI, that is, obtain 2L+1 sets of quadratic symmetric curves XQ l_LL -YI l_LL and the quadratic difference curve XQ l_L- -YI l_L- ; S600: According to the relative volume fraction V of phase a and phase b a and V b and the diffraction structure factor F a and F b , select the diffraction curves of phase a and phase b from several groups of diffraction curves; Step S600 includes the following steps: S601: For 2L+1 groups of quadratic symmetric curves XQ l_LL -YI l_LL Perform the integral operation to obtain 2L+1 group of integral results, recorded as ITG l_LL ; For the 2L+1 group of quadratic difference curves XQ l_L- -YI l_L- Perform the integral operation to obtain 2L+1 group of integral results, recorded as ITG l_L- ; S602: According to ITG l_LL and ITG l_L- Calculate the deviation value δ of 2L+1 group l ; S603: Select 2L+1 groups of deviation values ​​δ l The minimum value in is denoted as ,but The corresponding quadratic symmetry curve and quadratic asymmetric curve These are the diffraction curves of phase a and phase b, denoted as XQ a -YI a and XQ b -YI b .

2. The method according to claim 1, wherein: In step S200, the diffraction structure factor F a Calculated by the following formula: ； The diffraction structure factor F b Calculated by the following formula: ； Where n is the different positions occupied by the basic unit, n=1, 2, ..., N, N is the total number of positions occupied by the basic unit constituting the unit cell; π is the circumference of a circle; i is the symbol for an imaginary number in mathematics; hkl is the Miller index, indicating that the crystal plane where diffraction occurs is (hkl), and the value ranges of h, k, and l are all integers in the interval [0, ∞]; u n 、v n 、w n are the horizontal, vertical and vertical coordinates of the position n occupied by the basic unit, and u n 、v n 、w n The value range of f is a real number in the interval [0, 1]; n is the scattering factor of the basic unit.

3. The method according to claim 2, wherein: The scattering factor f n Calculated by the following formula: ； Where m is the smallest unit constituting different positions n, and m=1, 2, ..., M, M is the number of smallest units; f n,m is the scattering factor of the smallest unit m; φ n,m is the probability of the smallest unit m appearing in different positions n, and satisfies the relationship .

4. The method according to claim 1, wherein: In step S602, the deviation value δ is calculated by the following formula: l : ； Among them, V a and V b are the relative volume fractions of phase a and phase b, F a and F b are the diffraction structure factors of phase a and phase b, respectively.

5. The method according to claim 1, wherein: In step S400, any function including a polynomial function P(x), a Gauss function G(x), a Lorentz function L(x) and a Voigt function V(x) is used to fit the diffraction vector modulus length-diffraction intensity curve xq-yi, wherein: The polynomial function P(x) is expressed as: ； The Gauss function G(x) is expressed as: ； The Lorentz function L(x) is expressed as: ； The Voigt function V(x) is expressed as: ； Among them, a0, a1, a2, a n-1 , a n , A, B, C, A', B', C', σ, γ are the coefficients of the function, e is a natural number, and π is the ratio of a circle to a circle.

6. A computer comprising: Memory, for storing computer instructions; A processor, configured to execute computer instructions to implement the method described in any one of claims 1 to 5.

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