CN108959709B - Grain boundary structure searching method based on defect property and multi-scale simulation - Google Patents
Grain boundary structure searching method based on defect property and multi-scale simulation Download PDFInfo
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Abstract
The invention discloses a grain boundary structure searching method based on defect property and multi-scale simulation, which belongs to the technical field of nuclear material irradiation damage simulation. Compared with the existing simulation method, the method considers the occupation and evolution processes of the defects, and has more physical significance.
Description
Technical Field
The invention belongs to the technical field of nuclear material irradiation damage simulation, and particularly relates to a grain boundary structure searching method based on defect properties and multi-scale simulation.
Background
When the material is irradiated by high-energy particles (such as neutrons and ions), irradiation defects such as vacancies and self-interstitial atoms are generated. These irradiation defects often segregate to defect traps such as grain boundaries, which may alter their structure. There are two possible ways in which defects and grain boundaries can act. On one hand, the grain boundary has a determined structure and can be used as the background of defect motion, and the defects can be diffused and clustered; on the other hand, the defect causes the change of the grain boundary structure, so that the phase transformation of the grain boundary occurs, and the defect finally becomes a part of the grain boundary structure, thereby losing the property of the defect. The current method for searching the grain boundary structure only considers the arrangement and combination of lattice points from the geometric point of view. In fact, for a given grain boundary structure, the defects have fixed lattice point positions, and at a certain temperature, the evolution of the defects is a multi-scale process. Therefore, it is necessary to develop a grain boundary structure search algorithm based on defect properties and multi-scale simulation to simulate the irradiation defect induced grain boundary structure change process.
Disclosure of Invention
In order to solve the problems, the invention provides a grain boundary structure searching method based on defect properties and multi-scale simulation, which is suitable for researching a grain boundary structure change process induced by irradiation defects.
The invention is realized by adopting the following technical scheme:
the invention provides a grain boundary structure searching method based on defect properties and multi-scale simulation, which comprises the following steps of:
step S1: establishing an initial grain boundary model according to a barycentric lattice theory and relaxing the model; calculating lattice point defect forming energy near the grain boundary, and determining the most stable occupation position of the defect according to the position where the minimum defect forming energy is located;
step S2: determining the size, the atomic coordinates and the defect occupation coordinates of the structural unit of the minimum grain boundary structure;
step S3: setting the minimum structural unit copying number in the direction parallel to the grain boundary;
step S4: copying the occupied coordinates of the defects, copying the coordinates of the minimum structure unit, and generating a random occupied sequence of the defects;
step S5: for a certain occupation sequence, modifying atomic coordinates in the structural unit;
step S6: setting relative sliding step length and step number of crystal grains in the direction parallel to the grain boundary;
step S7: relative slip grains for a certain amount of slip;
step S8: relaxing the sliding grain boundary model;
step S9: calculating grain boundary energy density, firstly judging whether the maximum slippage has been reached, returning to the step S7 to displace the crystal grains again if the maximum slippage has not been reached, judging whether all the defect sequences have been traversed or not if the maximum slippage has been reached, returning to the step S5 to revise original atomic coordinates in the structural unit again if all the defect sequences have not been traversed, and outputting a defect proportion, minimum grain boundary energy density and a grain boundary structure corresponding to the defect sequences if all the defect sequences have been traversed;
step S10: judging whether the number of structural unit copies has been traversed, if so, ending the process, otherwise, returning to the step S3, and resetting the minimum number of structural unit copies in the direction parallel to the grain boundary.
The method only considers the occupation situation of the defects, does not consider the clustering process of the defects, and if the defect occupation property and the defect clustering process are considered, the method further comprises the following steps after step S5: the configuration was relaxed using the lattice point kinetics monte carlo (LKMC) method.
Preferably, the first and second electrodes are formed of a metal,
before the LKMC method is used for relaxing the configuration, a defect transition rate table near an interface needs to be constructed in advance.
A method of relaxing a configuration by the LKMC method, comprising:
step S501: for a given interface, establishing a mapping between LKMC grid points and defect states; for the vacancy, the lattice topological pattern in the LKMC is the same as the actual atomic lattice of the grain boundary, and the corresponding atomic number is the lattice number in the LKMC; for self-interstitial atoms, the LKMC crystal lattice and the atom crystal lattice have a translation relation, the self-interstitial atoms are usually condensed to the same state after the structure near the crystal boundary is relaxed, and the same state transition is avoided by judging the distance between the relaxed self-interstitial states;
step S502: establishing a transition rate table among different defect states, calculating all atomic lattice points between the defect states and the defect states, and calculating energy barriers of all states of vacancy atoms and interstitial atoms on the LKMC lattice by adopting an NEB method (standard method for calculating transition states), namely forward and backward transition energy barriers of an area near an interface along all transition paths, and further converting the energy barriers into corresponding rates.
In step S2, the defect formation energy Ef is calculated by:
Ef＝E2-E1±Ecoh
wherein E is1And E2Perfect grain boundaries and grain boundaries containing defects, respectively, are always present, and Ecoh is the lattice cohesive energy in the bulk.
In step S9, the grain boundary energy density γ calculation method includes:
γ＝(E-E0)/S
wherein E is the atomic energy of the grain boundary core region, E0The energy of the bulk region with the same atomic number as that of E, S is the area of the grain boundary, and is the product of the model sizes in two directions parallel to the grain boundary.
The invention has the beneficial effects that: the invention provides a grain boundary structure searching method based on defect property and multi-scale simulation. Compared with the existing simulation method, the method considers the occupation and evolution processes of the defects, and has more physical significance.
Drawings
FIG. 1 is a flow chart of the algorithm of the present invention, considering only the defect occupancy;
FIG. 2 is a schematic diagram of defect occupation and evolution and its effect on grain boundary structure, wherein light gray globules represent energetically unfavorable defect occupation positions in the grain boundary core region, dark gray globules represent defect occupation positions, and the defect occupation positions are represented by light gray squares. The structure in the rounded box in M0 indicates the initial smallest structural unit of the grain boundary, and a plurality of structural units represent the replication process; m1 illustrates the replication process of a building block containing a defect; m2 illustrates that multiple defects are randomly generated after the structural elements are copied; m3 illustrates the multiple defect clustering results generated;
FIG. 3 is a flow chart of the algorithm of the present invention, taking into account both the defect occupancy and the defect diffusion clustering process;
FIG. 4 is a plot of energy density of iron-tilt symmetric grain boundaries sigma 5(310)/[001] and structure as a function of defect occupancy ratio calculated using the algorithm of the present invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further explained below by combining the specific drawings.
Example 1
The embodiment provides a grain boundary structure searching method based on defect properties and multi-scale simulation, as shown in fig. 1 and 2(M0-M2), and when only the occupation situation of the defects is considered, the method comprises the following steps:
step S1: establishing an initial grain boundary model with a certain size according to a repositioning lattice theory, and relaxing the initial grain boundary model, wherein the model size in the step of perpendicular grain boundary suggests 2 nanometers;
calculating lattice defect forming energy within a range of 1 nanometer near a grain boundary, wherein the defect forming energy Ef is calculated by the following method:
Ef＝E2-E1±Ecoh
wherein E is1And E2Respectively, perfect crystal boundary and total energy of the crystal boundary containing defects, and Ecoh is lattice point cohesive energy in the block;
and obtaining the position where the minimum defect forming energy is located according to the grid point defect forming energy near the grain boundary obtained by calculation, and taking the position as the most stable occupied position of the defect.
Step S2: and determining the minimum grain boundary structural unit size box0 and box1, and determining the atom coordinate cor and the defect occupation coordinate all _ V in the minimum structural unit by searching atoms and defects with the coordinates in the range of [0, box0], [0, box1] in the relaxed grain boundary model.
Step S3: in order to expand the minimum structural unit and the defect coordinate and randomly generate a certain number of defects, firstly, setting minimum structural unit copy numbers M1 and M2 in the direction parallel to the grain boundary;
step S4: copying a minimal structural unit coordinate cor, copying a defect occupation coordinate all _ V, and respectively translating coordinates in two directions parallel to grain boundaries in cor and all _ V (0-M)1-1) xbox 0 and (0-M)2-1) xbox 1, then update cor and all _ V to the translated coordinates;
and for the number M of the defect occupied positions after copying, generating a defect random occupied sequence of different random integer sequences of 1-M by adopting a matlab function randderm:
step S5: modifying atomic coordinates in the structural unit for a certain occupation sequence, wherein for vacancy type defects, lattice points occupied by vacancies are deleted, and for interstitial type defects, atoms are inserted in interstitial positions;
step S6: setting relative slip step length dx, dy and step number Nx, Ny of crystal grains in the direction parallel to the grain boundary, wherein the relationship between the step length and the step number and the size px, py of the periodic unit in the direction parallel to the grain boundary is Nx ═ px/dx and Ny ═ py/dy, and the step length dx and dy are usually taken as
In principle, does not exceed the distance between two neighboring states.
Step S7: relative slip grains for a certain amount of slip;
step S8: fully relaxing the slipped grain boundary model by adopting a steepest descent method;
step S9: calculating the grain boundary energy density gamma:
γ＝(E-E0)/S
wherein E is the atomic energy of the grain boundary core region, E0The energy of the bulk region with the same atomic number as E, S is the area of the grain boundary, and is the model size in two directions parallel to the grain boundaryMultiplying;
and judging whether the crystal grains reach the maximum slippage, returning to the step S7 to displace the crystal grains again if the maximum slippage is not reached, judging whether all the defect sequences are traversed or not if the maximum slippage is reached, returning to the step S5 to revise the atomic coordinates in the structural unit again if all the defect sequences are not traversed, and outputting the defect proportion, the minimum grain boundary energy density and the grain boundary structure corresponding to the defect sequences if all the defect sequences are traversed.
Step S10: and judging whether the number of structural unit copies is traversed or not, if so, ending the process, and obtaining the minimum grain boundary energy and the corresponding structure, otherwise, returning to the step S3, and resetting the minimum number of structural unit copies in the direction parallel to the grain boundary.
Example 2
The embodiment provides a grain boundary structure searching method based on defect properties and multi-scale simulation, as shown in fig. 2(M0-M3) and 3, in the case that both the occupation properties of defects and the defect clustering process are considered, the method comprises the following steps:
step S1: establishing an initial grain boundary model with a certain size according to a repositioning lattice theory, and relaxing the initial grain boundary model, wherein the model size in the step of perpendicular grain boundary suggests 2 nanometers;
calculating lattice defect forming energy within a range of 1 nanometer near a grain boundary, wherein the defect forming energy Ef is calculated by the following method:
Ef＝E2-E1±Ecoh
wherein E is1And E2Respectively, perfect crystal boundary and total energy of the crystal boundary containing defects, and Ecoh is lattice point cohesive energy in the block;
and obtaining the position where the minimum defect forming energy is located according to the grid point defect forming energy near the grain boundary obtained by calculation, and taking the position as the most stable occupied position of the defect.
Step S2: and determining the minimum grain boundary structural unit size box0 and box1, and determining the atom coordinate cor and the defect occupation coordinate all _ V in the minimum structural unit by searching atoms and defects with the coordinates in the range of [0, box0], [0, box1] in the relaxed grain boundary model.
Step S3: in order to expand the minimum structural unit and the defect coordinate and randomly generate a certain number of defects, firstly, setting minimum structural unit copy numbers M1 and M2 in the direction parallel to the grain boundary;
step S4: copying a minimal structural unit coordinate cor, copying a defect occupation coordinate all _ V, and respectively translating coordinates in two directions parallel to grain boundaries in cor and all _ V (0-M)1-1) xbox 0 and (0-M)2-1) xbox 1, then update cor and all _ V to the translated coordinates;
and for the number M of the defect occupied positions after copying, generating a defect random occupied sequence of different random integer sequences of 1-M by adopting a matlab function randderm:
step S5: modifying atomic coordinates in the structural unit for a certain occupation sequence, wherein for vacancy type defects, lattice points occupied by vacancies are deleted, and for interstitial type defects, atoms are inserted in interstitial positions;
relaxing the configuration using the LKMC method, comprising:
step S501: for a given interface, a mapping between LKMC grid points and defect states is established. For the vacancies, the lattice topology pattern in the LKMC is the same as the actual atomic lattice of the grain boundary, and the corresponding atomic number is the lattice number in the LKMC. LKMC crystal lattice for self-gap atoms
With atomic lattice
There is a translation relationship (
Is a unit vector oriented along self-interstitial atoms), and the self-interstitial atoms are usually condensed to the same state after the structure near the grain boundary is relaxed, and the transition of the same state is avoided by judging the distance between the self-interstitial states after the relaxation;
step S302: a table of transition rates between different defect states is built. And calculating all atomic lattice points between the first neighbor and the second neighbor, and calculating energy barriers for the transition of the vacancy atoms and the interstitial atoms between all states on the LKMC crystal lattice by adopting an NEB method, namely forward and backward transition energy barriers of the region near the interface along all transition paths, so as to convert the vacancy atoms and the interstitial atoms into corresponding rates.
Step S6: setting relative slip step length dx, dy and step number Nx, Ny of crystal grains in the direction parallel to the grain boundary, wherein the relationship between the step length and the step number and the size px, py of the periodic unit in the direction parallel to the grain boundary is Nx ═ px/dx and Ny ═ py/dy, and the step length dx and dy are usually taken as
In principle, does not exceed the distance between two neighboring states.
Step S7: relative slip grains for a certain amount of slip;
step S8: fully relaxing the slipped grain boundary model by adopting a steepest descent method;
step S9: calculating the grain boundary energy density gamma:
γ＝(E-E0)/S
wherein E is the atomic energy of the grain boundary core region, E0The energy of the block region with the same atomic number as E, S is the area of the grain boundary, and is the product of the sizes of models parallel to the grain boundary in two directions;
judging whether the crystal grains reach the maximum slippage, if not, shifting the crystal grains again in the step S7, if so, judging whether all the defect sequences are traversed, if not, shifting the crystal grains to the step S5 to revise the atomic coordinates in the structural unit, and if so, outputting the defect proportion, the minimum grain boundary energy density and the grain boundary structure corresponding to the defect sequences
Step S10: and judging whether the number of the structural unit copies is traversed or not, if so, ending to obtain the minimum grain boundary energy and the corresponding structure, otherwise, turning to the step S3, and resetting the minimum number of the structural unit copies in the direction parallel to the grain boundary.
The algorithm of the invention is adopted to calculate the relation between the energy density and the structure of a tilting symmetrical grain boundary sigma 5(310)/[001] of the iron and the occupation proportion of the defect, and the result is shown in figure 4, which shows that the energy density of the grain boundary is related to the occupation proportion of the defect, the energy density of the grain boundary can be reduced by a sliding grain boundary, and the structure of the grain boundary is changed after the defect is contained in the grain boundary. The grain boundary structure under different defect proportions can be obtained by adopting the algorithm of the invention. The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (6)
1. A grain boundary structure searching method based on defect property and multi-scale simulation is characterized by comprising the following steps:
step S1: establishing an initial grain boundary model according to a barycentric lattice theory and relaxing the model; calculating lattice point defect forming energy near the grain boundary, and determining the most stable occupation position of the defect according to the position where the minimum defect forming energy is located;
step S2: determining the size, the atomic coordinates and the defect occupation coordinates of the structural unit of the minimum grain boundary structure;
step S3: setting the minimum structural unit copying number in the direction parallel to the grain boundary;
step S4: copying the occupied coordinates of the defects, copying the coordinates of the minimum structure unit, and generating a random occupied sequence of the defects;
step S5: for a certain occupation sequence, modifying atomic coordinates in the structural unit;
step S6: setting relative sliding step length and step number of crystal grains in the direction parallel to the grain boundary;
step S7: relative slip grains for a certain amount of slip;
step S8: relaxing the sliding grain boundary model;
step S9: calculating grain boundary energy density, firstly judging whether the maximum slippage has been reached, returning to the step S7 to reset the slippage and displace the crystal grains if the maximum slippage has not been reached, judging whether all defect sequences have been traversed or not if the maximum slippage has been reached, returning to the step S5 to reset an occupation sequence if all defect sequences have not been traversed, modifying atomic coordinates in a structural unit, and outputting a defect proportion corresponding to the defect sequences, the minimum grain boundary energy density and a grain boundary structure if all the defect sequences have been traversed;
step S10: and judging whether the number of structural unit copies is traversed or not, if so, ending the process, and obtaining the minimum grain boundary energy and the corresponding structure, otherwise, returning to the step S3, and resetting the minimum number of structural unit copies in the direction parallel to the grain boundary.
2. The method for searching the grain boundary structure based on the defect property and the multi-scale simulation of claim 1, further comprising the step of, after the step S5: the configuration was relaxed using the lattice point kinetic monte carlo method.
3. The method for searching the grain boundary structure based on the defect property and the multi-scale simulation as claimed in claim 2, wherein a defect transition rate table near the interface is constructed in advance before the configuration is relaxed by using a lattice point dynamics Monte Carlo method.
4. The method for searching the grain boundary structure based on the defect property and the multi-scale simulation as claimed in claim 3, wherein the method for relaxing the configuration by the lattice point dynamics Monte Carlo method comprises the following steps:
step S501: for a given interface, establishing mapping between lattice point dynamics Monte Carlo LKMC lattice points and defect states;
step S502: and establishing a transition rate table among different defect states, calculating all atomic lattice points between the first neighbor and the second neighbor, and calculating energy barriers for all states of vacancy and interstitial atoms on the LKMC lattice by adopting an NEB method so as to convert the vacancy and interstitial atoms into corresponding rates.
5. The method for searching the grain boundary structure based on the defect property and the multi-scale simulation as claimed in any one of claims 1 to 4, wherein in the step S2, the defect formation energy Ef is calculated by:
wherein the content of the first and second substances,E 1 andE 2 respectively perfect grain boundaries and grain boundaries containing defects,Ecohis the lattice point cohesive energy in the block.
6. The method for searching the grain boundary structure based on the defect property and the multi-scale simulation as claimed in any one of claims 1 to 4, wherein in the step S9, the grain boundary energy density calculation method comprises:
whereinEIs the atomic energy of the core region of the grain boundary,E 0 is the same asEThe energy of the bulk region of the same atomic number,Sthe grain boundary area is the product of the model sizes in two directions parallel to the grain boundary.
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