A method of predicting formability of max phase materials

Abstract

The application belongs to the field of material science, and provides a method for predicting formability of MAX phase materials, which selects characteristic factors affecting material structure, designs characteristic factor expression according to material structure, designs a characteristic model affecting MAX phase structure on the premise of the selected characteristic factors, constructs a structure mapping atlas, realizes that experimental synthesis MAX phase and unformable MAX phase are distributed according to different regions in the structure mapping atlas, and provides guidance for searching new MAX phase. The method is a relatively successful method for structure prediction without the help of experimental assistance. The method provided by the application can greatly reduce the consumption of artificial experiment and first principle calculation resources, save cost, and provide theoretical guidance for synthesizing high-performance MAX phase materials.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of material science, and particularly relates to a method for predicting formability of MAX phase materials. BACKGROUND

[0002] There is a close relationship between the structure and performance of materials; therefore, the analysis and research on the structure run through the whole course of the development of material science, and will continue to occupy an important position in the research of material science. At the same time, the acquisition and determination of the structure information of materials are also the prerequisite and key step for further understanding and modeling analysis of the performance of various materials.

[0003] MAX phase is a large class of new easy-to-process layered carbides, nitrides and carbonitrides, with a general chemical formula Mn+1AXn. Wherein M is an early transition metal, A is usually a group A element, X is usually C or N, and n is mostly 1-3. MAX phase materials have been widely concerned due to their metal and ceramic characteristics; so far, nearly 170 MAX phases have been successfully prepared, and new MAX phase materials are still being discovered and reported. In order to further accelerate the discovery of this kind of materials, a database containing all the information of MAX phase materials can be constructed, and on this basis, effective criteria for judging the formability of MAX phase can be extracted. Researchers construct a two-dimensional structure mapping diagram, aiming to demarcate the characteristic domain of the formability of MAX phase, and obtain understanding and explanation from the micro theory; and then provide theoretical guidance for searching new MAX phase.

[0004] Current methods to predict formability include experimental characterization methods, first-principles computational modeling, machine learning methods, and structure mapping methods: 1) Experimental characterization: This method is the core indicator for determining formability; however, even with the introduction of high-throughput and automated methods today, this method is still time-consuming and expensive to test, especially in terms of a large number of potential material synthesis; 2) First-principles computational modeling: With the development of computers and the invention of single-electron potential calculation methods that simplify many-body interactions, it is possible to calculate and predict material structures through quantum mechanical principles. This method predicts the formability of materials by calculating the interactions between atoms in a substance, but due to the high complexity of first-principles calculations, it requires a large amount of computing resources and still has certain limitations for high-precision prediction; 3) Machine learning methods: With the rapid development of computer hardware and software technology and the increasing size of materials databases, machine learning can extract effective information from a large amount of material data and effectively extract the implicit rules and correlations in the data set to predict the formability of materials, but machine learning has weak physical interpretability and is difficult to be accepted by material experimental researchers; 4) Structure mapping method: By analyzing the key factors that determine the formability of a specific material, a two-dimensional structure mapping diagram is constructed to distinguish between formable and non-formable materials. Although the structure mapping method starts from the properties of materials and elements and has good interpretability, the determination of characteristic factors requires a thorough understanding of materials by experimental researchers, and the current structure mapping diagram has not achieved good results in predicting the formability of MAX phases, with many singular points.

[0005] Chinese Patent CN111274691A discloses a method for predicting the formability of MAX phase materials by establishing a size factor characteristic equation based on the covalent atomic radius of M-site elements, the covalent atomic radius of A-site elements, and the stoichiometric ratio of corresponding position elements. However, the factors considered by this method are not comprehensive enough for the continuous development of existing MAX phase materials. SUMMARY

[0006] The technical problem to be solved by the present application is to provide a method for predicting the formability of MAX phase materials, which solves the problems of long time-consuming, high testing cost, and low prediction accuracy in crystal structure stability prediction methods.

[0007] To achieve the above purpose, the technical scheme adopted by the present application is:

[0008] A method for predicting the formability of MAX phase materials, comprising the following steps:

[0009] S1, selecting characteristic factors affecting the stability of the crystal structure of the MAX phase according to the alloy law, the geometric structure of the MAX phase, and the electronic structure of the MAX phase, the characteristic factors including an electron concentration factor E and a geometric structure factor R;

[0010] S2, designing an expression of the characteristic factors according to the characteristics of the structure of the MAX phase material based on the selected characteristic factors, and establishing a structure mapping model for predicting the formability of the MAX phase; the designed expression of the electron concentration factor is determined by the number of valence electrons or the number of delocalized electrons of the M-site, X-site and A-site elements, and the designed expression of the geometric structure factor is determined by the radii of the atoms of the M-site, A-site and X-site elements and the number n of layers of the MX octahedron.

[0011] S3, calculating a structure mapping atlas based on the non-stable and experimentally synthesized MAX phase structures;

[0012] S4, inputting the physical parameters of the potential MAX phase constituent elements into the structure mapping model obtained in step S2, outputting a data set from the structure mapping model, visualizing the data set in the structure mapping atlas of step S3, and exploring the potential formable MAX phase material.

[0013] Preferably, the designed expression of the electron concentration factor is:

[0014]

[0015] wherein VEC M is the number of valence electrons of the M-site element, (e / a)A represents the number of delocalized electrons of the A-site element, VEC X is the number of valence electrons of the X-site element, nM, n A , and n X represent the atomic coefficients of the M-site, A-site and X-site elements, respectively.

[0016] Preferably, the designed expression of the geometric structure factor is:

[0017]

[0018] wherein RM, R A , and R X are the covalent atomic radii of the M-site element, A-site element and X-site element, respectively, and n is the number of layers of the MX octahedron in each unit cell of the MAX phase.

[0019] Preferably, the stable MAX phase in step S3 is an experimentally synthesized stable MAX phase.

[0020] Preferably, the structure mapping atlas in step S3 is constructed according to the non-stable 211-MAX phase and the experimentally synthesized 211-MAX phase.

[0021] Preferably, the step S3 further comprises the following step: verifying the structure mapping atlas; the verification method is as follows: verifying the structure mapping atlas by using first principle to calculate the non-stable 312-MAX phase and 413-MAX phase, and the 312-MAX phase and 413-MAX phase that have been synthesized in experiments.

[0022] Compared with the prior art, the present application has at least the following beneficial effects:

[0023] (1) The present application provides a method for analyzing and predicting the formability of MAX phase materials, which measures the formability of the MAX phase by constructing a two-dimensional structure mapping atlas, delimits the characteristic domain of the MAX phase, and extracts the effective criterion for judging the formability of the MAX phase, thereby providing a guiding principle for searching for new MAX phases;

[0024] (2) The present application determines the characteristic factors that affect the formability of MAX phase materials according to the properties and structure of the MAX phase materials, and designs the characteristic factor expression, which takes into account the four main elements of the MAX phase (M-site element, A-site element, X-site element, and MX octahedral layer number n) to improve the prediction efficiency of the formability of the MAX phase materials;

[0025] (3) For an unknown MAX phase, the formability of the unknown MAX phase can be quickly and effectively obtained through the constructed structure mapping atlas of the formability of the MAX phase, which can further be used to predict the unknown structure of new materials and provide a reference for experimental researchers; for a MAX phase that is difficult to synthesize, the MAX phase can be synthesized by adjusting the elements and proportions to adjust the values of the geometric structure factor R and the electronic structure factor E of the MAX phase according to the structure mapping method, and some elements that were previously difficult to add to the MAX phase materials can be added through this strategy. This method does not require experimental assistance for structure prediction. Moreover, the method provided by the present application can greatly reduce the consumption of manual and computing resources, save costs, and provide a theoretical guidance for synthesizing high-performance MAX phase materials. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 is a flowchart of a method for predicting the formability of a MAX phase according to an embodiment of the present application;

[0027] Figure 2 is a two-dimensional structure mapping atlas constructed based on the model equation in step S2 to calculate the 211-MAX phase parameters in step S3 according to an embodiment of the present application;

[0028] Figure 3is the accuracy of the structure diagram verified in step S4 in the embodiment provided by the application based on the model equation in S2 to calculate 312-MAX phase after verification;

[0029] Figure 4 is the accuracy of the structure diagram verified in step S4 in the embodiment provided by the application based on the model equation in S2 to calculate 413-MAX phase after verification;

[0030] Figure 5 is the strategy in the example provided by the application to make the MAX phase difficult to form formable by adjusting the element composition. DETAILED DESCRIPTION

[0031] The following is a specific embodiment of the application, and the technical solutions of the application are further described in conjunction with the drawings. However, the application is not limited to these embodiments.

[0032] Reference Figures 1-5 A method for predicting the formability of MAX phase, comprising the following steps:

[0033] S1: selecting characteristic factors affecting the stability of the crystal structure of MAX phase;

[0034] Specifically, the following two characteristic factors are selected in this step S1 based on the alloy law, the geometric structure and the electronic structure of the MAX phase: the electronic concentration factor E and the geometric structure factor R.

[0035] S2: Based on the selected characteristic factors, according to the characteristics of the structure of the MAX phase material, design the expression of the characteristic factors, and establish a structure mapping model for predicting the formability of the MAX phase:

[0036] The electronic concentration effect is crucial in complex materials, and the electronic concentration controls the phase stability and many physical properties of the compound. The MAX phase material has a complex way of electronic interaction between constituent elements. Considering the metallic nature of M-A bonding, the Hume-Rothery theory is used to distinguish the factors affecting the formation of compounds and controlling the alloying behavior, thereby analyzing the formability of the MAX phase. In nearly 90 years, Hume-Rothery rules have been used to focus on three particularly important aspects of alloying, size factor, electronic concentration factor and electrochemical factor, and the electronic concentration factor indicates that a certain crystal structure will appear at a certain characteristic electronic concentration; This means that similar structures will appear at different electron / atom ratios. Barsoum also mentioned in his research that the formability of MAX phase materials can be observed from the average number of valence electrons n val of a given MAX phase. The electronic concentration coefficient is used as a characteristic factor in the application.

[0037] Currently, the electron concentration can be defined by two different parameters: one is the number of valence electrons per atom (e / a); the other is the number of valence electrons (VEC), which includes the number of d electrons accommodated in the valence band. e / a and VEC play an important role in the process of chemical bond formation of compounds and are closely related. The main difference between them is that the definition of e / a is based on the assumption that "free" electrons are uniformly distributed on the crystal, while VEC is locally defined for a single constituent element in real space.

[0038] In MAX phases, the M-A bond is metallic, which is weaker than the covalent M-X bond. In fact, the d electrons of M atoms interact with the p electrons of X atoms (carbon and / or nitrogen), and the sharing of electron pairs between these atoms forms strong covalent bonds. In the M-A bond, the interaction between the d electrons of M atoms and the p electrons of A atoms does not form a strong covalent bond, which is the reason why the M-A bond is weaker than the M-X bond. Considering the special bonding characteristics of MAX phases, both VEC and e / a values need to be used.

[0039] According to the above analysis, here we select VEC (number of valence electrons) for M-site and X-site elements and e / a (number of valence electrons) for A-site elements to calculate the overall electron concentration of MAX phases. The constructed electron concentration factor expression is:

[0040]

[0041] where VEC M is the number of valence electrons of M-site elements, (e / a) A represents the number of valence electrons of A-site elements, VEC X is the number of valence electrons of X-site elements, nM, n A , n X represent the atomic coefficients of M-site, A-site, and X-site elements, respectively.

[0042] The values of the number of valence electrons of M-site and X-site elements and the number of valence electrons of A-site elements are as follows:

[0043]

[0044]

[0045] where the atomic radii values of M-site, A-site, and X-site are as follows:

[0046]

[0047]

[0048] The values finally taken in this step S2 will be used in the present example Figure 2 ,Figure 3 、 Figure 4 、 Figure 5 The calculation of the characteristic quantity.

[0049] And the expression of the geometric structure factor mainly includes octahedral factor and intercalation factor. The octahedral factor, which measures the ability of X atoms to embed in the octahedron, if the X-site atoms want to form octahedral coordination with M-site atoms, the ratio of their radii should be within a certain range.

[0050] And for the intercalation factor, the original internal prism will change due to the A-site element entering the gap position, and if the size difference is large, it will cause the change of distortion energy and then seriously affect the stability of MAX phase, so the influence of A atoms on the structure of MAX phase needs to be considered. In the MAX phase, the A-site atoms are inserted into the MX octahedron in the form of atomic layers, so when considering how the A-site elements affect the stability of the MAX phase, the comparison between the atomic radius of the A-site elements and the thickness of the entire MX octahedral atomic layer should be considered. The ideal state of the thickness of the MX octahedral atomic layer is So the expression of the intercalation factor is

[0051] The geometric structure factor R needs to combine the octahedral factor and the intercalation factor to consider the combination mode between the M6X atomic layer and the A atomic layer in the 211-MAX phase. In the 211-MAX phase, one layer of MX octahedral atomic layer is combined with A atomic layer above and below, that is, the A atomic layer can be intercalated in the upper and lower directions of the MX octahedral atomic layer, so the ratio of the intercalation factor to the octahedral factor should be 2:1. Therefore, the geometric structure factor in the 211-MAX phase is preliminarily designed as:

[0052]

[0053] In the 312-MAX phase, two layers of MX octahedral atomic layers are contained in one unit cell, so the A atomic layer is intercalated in three different positions (above the octahedral atomic layer, between the octahedral atomic layers, and below the octahedral atomic layer), so the ratio of the intercalation factor to the octahedral factor should be 3:2.

[0054] Similarly, in the 413-MAX phase, the ratio of the intercalation factor to the octahedral factor is 4:3. Therefore, the geometric structure factor is preliminarily designed to represent the ratio of the intercalation factor to the octahedral factor in the 211-MAX phase, 312-MAX phase and 413-MAX phase with n as the weight coefficient, which can be expressed as:

[0055]

[0056] However, the preliminary design of the geometric structure factor also has a problem: as n increases, the coefficient of the two geometric structure factors also increases, resulting in the geometric structure factor of MAX phases with large n values (such as 413-MAX phases) being much larger than that of MAX phases with small n values (such as 211-MAX phases). This causes MAX phases with different n values to fall into different regions of the phase separation of the structure map, making it difficult to divide the MAX phase formable / non-formable regions. In order to make all MAX phases formable fall into the same region of the structure map, a normalization factor is introduced while keeping the ratio of the two geometric structure factors unchanged, and the final geometric structure factor is designed as:

[0057]

[0058] In the present application, the stability of the MX octahedron itself and the influence of the A-site atom on the overall structure of the MAX phase are comprehensively considered, and the octahedral factor and the intercalation factor are designed and combined to form the geometric structure factor. The factor expression takes into account the influence of the number of layers n, and the ratio of the two geometric structure factors is adjusted according to the different n, thereby reflecting the proportion of the MX octahedron in the structure of the MAX phase. As n increases, the proportion of the MX octahedron in the overall MAX phase gradually increases, and the final geometric factor also well reflects this point (as n increases, the coefficient of the octahedral factor increases from 1 / 3 to 2 / 5 and 3 / 7):

[0059] In addition, the normalization factor is used to correct the values of the geometric structure factor expressions of MAX phases with different n, providing convenience for distinguishing MAX phases that can be formed / non-formed in the same region in the future.

[0060] S3: Constructing a structure map based on the first-principle non-stable and experimentally synthesized MAX phases;

[0061] Figure 2 For the two-dimensional structure map drawn after calculation of the samples selected in this embodiment, it can be clearly seen that there are a left upper synthesis region and a right lower non-synthesis region, effectively distinguishing the 211-MAX phase that has been synthesized experimentally and the 211-MAX phase that cannot be synthesized by the first-principle, and the number of singular points is small.

[0062] After step S3, the following steps are further included: verifying the structure map, and the verification method is as follows: calculating the non-stable 312-MAX phase and 413-MAX phase by the first-principle, as well as the 312-MAX and 413-MAX phases that have been synthesized experimentally, and verifying the structure map.

[0063] S4: input the physical parameters of potential MAX phase constituent elements into the structure mapping model obtained in step S2, the structure mapping model outputs a data set, and the data set is visualized in the structure mapping map in step S3 to explore potential MAX phase materials that can be formed.

[0064] The experiments selected in this example have synthesized 312-MAX and 413-MAX phase samples by calculating the expressions proposed in step S2. Figure 3 and Figure 4 It can be seen that all the synthesized regions are located in Figure 2 the structure mapping map, and the first-principle calculation of the unstable 312-MAX and 413-MAX phase samples falls in the non-synthesizable region of the structure mapping map, verifying the accuracy of the structure mapping map. Figure 2

[0065] Referring to Figure 5 , by adjusting the element composition of the MAX phase, the electronic concentration factor E and the geometric structure factor R of the MAX phase are controlled, so that the MAX phase that is difficult to synthesize becomes synthesizable. For example, due to the high valence electron number of Mo (valence electron number is 6), the 312-MAX phase containing Mo is mostly in the non-forming region (the average electron concentration of Mo3AlC2 is 4.83), but combined with other low-valence M elements (such as Sc, Ti), the average electron concentration of the material is reduced, and the structure mapping map coordinates fall into the formable region of the structure mapping map. The ordered MAX phase containing Mo, Mo2ScAlC2 (average electron concentration 4.33) and Mo2TiAlC2 (average electron concentration 4.5), has been synthesized.

[0066] The specific embodiments described herein are merely illustrative of the spirit of the present application. Those skilled in the art to which the present application belongs can make various modifications or supplements to the described specific embodiments or replace them with similar ways, but will not deviate from the spirit of the present application or exceed the scope defined by the appended claims.​

Claims

1. A method for predicting the formability of MAX phase materials, characterized in that, Includes the following steps: S1. Based on the alloy law, the geometric structure of the MAX phase, and the electronic structure of the MAX phase, select characteristic factors that affect the stability of the MAX phase crystal structure. The characteristic factors include the electron concentration factor E and the geometric structure factor R. S2. Based on the selected characteristic factors, according to the characteristics of the MAX phase material structure, design characteristic factor expressions and establish a structure mapping model for predicting the MAX phase formation capability; the designed electron concentration factor expression is determined by the number of valence electrons or itinerant electrons of the M-site, X-site and A-site elements, and the designed geometric structure factor expression is determined by the atomic radius of the M-site, A-site and X-site elements and the number of MX octahedral layers n. S3. Calculate the structure mapping map of the MAX phase based on first-principles instability and experimentally synthesized phases; S4. Input the physical parameters of the potential MAX phase constituent elements into the structure mapping model obtained in step S2. The structure mapping model outputs a dataset. Visualize the dataset in the structure mapping spectrum in step S3 to explore the potential MAX phase materials that can be formed. The designed expression for the electron concentration factor is: Among them, VEC M It represents the number of valence electrons in the M-position element (e / a). A VEC represents the number of itinerant electrons in the A-position element. X It is the number of valence electrons of the element at position X, n M n A n X These represent the atomic coefficients of the M, A, and X positions, respectively. The expression for the designed geometric structure factor is: Among them, R M R A R X denoted as the covalent atomic radii of the elements at the M, A, and X positions, respectively, and n is the number of MX octahedral layers in each MAX phase unit cell.

2. The method for predicting the formability of MAX phase materials according to claim 1, characterized in that, The stable MAX phase mentioned in step S3 is the experimentally synthesized stable MAX phase.

3. The method for predicting the formability of MAX phase materials according to claim 2, characterized in that, In step S3, the structure mapping map is constructed based on the unstable 211-MAX phase and the experimentally synthesized 211-MAX phase.

4. The method for predicting the formability of MAX phase materials according to claim 1, characterized in that, Step S3 is followed by the following steps to verify the structure mapping spectrum. The verification method is as follows: the unstable 312-MAX and 413-MAX phases are calculated using first-principles calculations, as well as the experimentally synthesized 312-MAX and 413-MAX phases, to verify the structure mapping spectrum.

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