CN110033833A - A kind of unordered solid-solution material modeling method with chemical short feature - Google Patents
A kind of unordered solid-solution material modeling method with chemical short feature Download PDFInfo
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Abstract
The present invention relates to a kind of unordered solid-solution material modeling methods, the objective function of this method introducing description scheme short program situation, the objective function is constructed based on chemical short parameter, the complexity for avoiding special quasi- random structure method in the prior art can generate the unordered solid-solution material structure for meeting multiple chemical short parameter restrictive conditions.
Description
Technical field
The present invention relates to the modelings of unordered solid-solution material, more particularly to have the unordered solid-solution material of chemical short feature to model
Method.
Background technique
High performance alloys material is the material base of high-end manufacturing industry power strategy and the guide of hi-tech development.
As material usage condition is more harsh, the requirement to material property is also higher and higher.High performance alloys material is usually to add
Multiple common alloyings of element are realized.For the blindness and complexity for reducing alloy element addition, design of alloy pair
It is most important in research and development high-performance complex alloys material, it is to realize new material research and development from the traditional mode of experience guiding experiment to reason
By the key link of prediction, the new model transformation of experimental verification.
For using solid-solution material structure, for the practical engineering alloy of matrix, typical Local Structure feature is exactly molten
There are chemical shorts for the distribution of matter atom.Solute element is although occupy the lattice lattice position of solvent substrate, chemically ingredient
Angle can't determine the specific occupy-place of solute atoms, that is, there is chemical longrange disorder；But since solute atoms and matrix exist
Different degrees of reciprocation, thus there is the chemical short-range order distribution precision diffraction experiment confirmation for deviateing average structure, no
It is congruent to generate different topotaxial short program, influence the performance of solid-solution material alloy.
In the unordered solid-solution material such as alloy, there are above-mentioned chemical shorts.For the structure containing chemical short, mesh
Preceding common modeling scheme is and to introduce Cowley chemical short parameter using special quasi- random structure method.However it is existing
Modeling pattern have the disadvantage in that first is that method is not intuitive, the chemical short of structure can not be directly obtained；Second is that can not locate
There are many structures of the chemical short parameter of type for reason.
Summary of the invention
In view of the above-mentioned problems, the present invention provides a kind of unordered solid-solution material modeling method containing chemical short feature,
It is characterized by: this method introduces the objective function of description scheme chemical short situation, it is short that the objective function is based on chemistry
Program parameter building, the chemical short parameter are based on: in unordered solid-solution material modeling configuration, the first Elements Atom of distance
Meet the ratio of the ratio and second element atom of the second element atom at a preset positional relationship in entire configuration
And it constructs.
Further, the chemical short parameter is αj(ep,eq), meet formula (1) or formula (2):
Wherein, Pj(ep,eq) be for all elements symbol be epAtom jth neighbour's atom in, symbol of element eq
Atom ratio, cqFor e in entire configurationqThe ratio of Elements Atom；
Wherein, P 'j(ep, eq) be for all elements symbol be epAtom, from the 1st neighbour to all originals of jth neighbour
In son, symbol of element eqAtom ratio, cqFor e in entire configurationqThe ratio of Elements Atom.
Further, the gap based on the chemical short parameter and restrictive condition:
Construct the objective function；
Wherein,Indicate the chemical short parameter alpha in configuration σj(ep,eq)；
Wherein, WithRespectively
The preset chemical short parameter alphaj(ep,eq) minimum value and maximum value.
Further, the objective function are as follows:
Alternatively,
In above-mentioned formula (3), (4),Indicate the chemical short parameter alpha in configuration σj(ep,eq),
wj,p,qFor optional weight factor.
Further, the chemical short parameter is αr(ep, eq), meet formula (5) or formula (6):
Wherein, Pr(ep,eq) be for the symbol of element be epAll atoms, with these atomic distances be r atom
In, symbol of element eqAtom shared by ratio, cqFor e in entire configurationqThe ratio of Elements Atom；
Wherein, P 'r(ep, eq) indicate to be e for the symbol of elementpAll atoms, with these atomic distances less than r
In all atoms, symbol of element eqAtom shared by ratio, cqFor e in entire configurationqThe ratio of Elements Atom.
Further, the gap based on the chemical short parameter and restrictive condition:
Construct the objective function；
Wherein,Indicate the chemical short parameter alpha in configuration σr(ep, eq)；
Wherein, WithIt is respectively pre-
If the chemical short parameter alphar(ep, eq) minimum value and maximum value.
Further, the objective function are as follows:
Alternatively,
In above-mentioned formula (7), (8),Indicate the chemical short parameter alpha in configuration σr(ep, eq),
wj,p,qFor optional weight factor.
Further, further include the steps that objective function and chemical short parameter optimization:
Step (1): random to generate configuration σ；
Step (2): for each chemical short parameter in objective function, the chemical short under configuration σ is calculated
The specific value of parameter；
Step (3): if to each chemical short parameter, the chemical short parameter of configuration σ, which is all larger than, to be equal in advance
If the chemical short parameter minimum value, and be less than or equal to the preset chemical short parameter maximum value, then terminate pair
The optimization of chemical short parameter；Otherwise, step (4) are executed；
Step (4): two symbol of element e in random exchange configuration σpAnd eqThe coordinate position of different atom obtains
One new configuration σ '；Calculate the objective function ε (σ) and ε (σ ') of configuration σ and configuration σ '；
Step (5): if ε (σ ') < ε (σ), returns to step (2) based on configuration σ '；Otherwise, it is with configuration σ
Basis returns to step (4).
Further, above-mentioned all chemical short parameter values are all larger than equal to preset minimum value, and are less than etc.
The configuration corresponding to preset maximum value further executes the calculating and optimization of degree of disorder parameter；The degree of disorder parameter
Calculate and optimization based on SQS method perhaps SAE method or other can be in the method for description scheme longrange disorder feature；In nothing
In the optimization process of sequence degree parameter, all short distance order parameters of inspection structure only meet the structure of preset restrictive condition
Candidate structure of the energy as degree of disorder parameter optimization.Finally, it can obtain meeting short program ginseng by above optimization method
The highest material structure of the degree of disorder under the premise of number restrictive condition.
The invention has the beneficial effects that:
(1) modeling method of the invention avoids the complexity of special quasi- random structure method in the prior art, directly obtains
It obtains the chemical short of structure and is easily achieved.
(2) modeling method of the invention can generate the unordered solid solution for meeting multiple chemical short parameter restrictive conditions
Material structure efficiently realizes the optimization to chemical short parameter and structural disorder degree, obtains while having the chemical short distance of satisfaction
The solid-solution material structure of sequence and longrange disorder.
Detailed description of the invention
Fig. 1 is degree of disorder optimization process flow chart of the present invention in the case where applying short distance order parameter restrictive condition
Specific embodiment
In the description of the present invention, term " first ", " second ", " third " are used for description purposes only, and should not be understood as
Indication or suggestion relative importance.
1, chemical short parameter is defined
Modeling scheme used in the present invention is based on special quasi- random structure (SQS) method or similar atomic environment
(SAE) method or other description scheme longrange disorder degree methods.On the basis of the method, description scheme short distance is introduced
The objective function of sequence situation.The objective function is based on chemical short parameter, and Typical Representative is Cowley short distance order parameter.
Preferably, chemical short parameter of the invention is based on: in unordered solid-solution material modeling configuration, first yuan of distance
The ratio and second element atom that plain atom meets the second element atom at a preset positional relationship are in entire configuration
Ratio and construct.
Regular a: according to the ratio and second of second element atom in neighbour's atom site relationship of the first Elements Atom
Ratio of the Elements Atom in entire configuration and construct
The chemical short parameter of rule-based a building can be given as αj(ep,eq), meet formula (1) or formula (2):
Wherein, Pj(ep,eq) be for all elements symbol be epAtom jth neighbour's atom in, symbol of element eq
Atom ratio, cqFor e in entire configurationqThe ratio of Elements Atom；
Wherein, P 'j(ep, eq) be for all elements symbol be epAtom, from the 1st neighbour to all originals of jth neighbour
In son, symbol of element eqAtom ratio, cqFor e in entire configurationqThe ratio of Elements Atom.
In above formula (1), (2), if αj(ep,eq) less than 0, in epE around elementqAtomic ratio has been more than eqAtom
Ratio in system, epAnd eqElement is mutually " attraction "；And if αj(ep,eq) it is greater than 0, in epE around elementqAtomic ratio
Example is less than eqRatio of the atom in system, epAnd eqElement is mutually " repulsion ".
Regular b:According to the ratio and second of second element atom in the certain distance positional relationship of the first Elements Atom
Ratio of the Elements Atom in entire configuration and construct
The chemical short parameter of rule-based b building can be given as αr(ep, eq), meet formula (5) or formula (6):
Wherein, Pr(ep,eq) be for the symbol of element be epAll atoms, with these atomic distances be r atom
In, symbol of element eqAtom shared by ratio, cqFor e in entire configurationqThe ratio of Elements Atom；
Wherein, P 'r(ep, eq) indicate to be e for the symbol of elementpAll atoms, with these atomic distances less than r
In all atoms, symbol of element eqAtom shared by ratio, cqFor e in entire configurationqThe ratio of Elements Atom.
In above formula (5), (6), if αr(ep, eq) less than 0, in epE around elementqAtomic ratio has been more than eqAtom
Ratio in system, epAnd eqElement is mutually " attraction "；And if αr(ep, eq) it is greater than 0, in epE around elementqAtomic ratio
Example is less than eqRatio of the atom in system, epAnd eqElement is mutually " repulsion ".
It should be noted that above-mentioned rule a, b it is preferred that present but it is not limited to this, be actually based on " distance
The ratio and second element atom that first Elements Atom meets the second element atom at a preset positional relationship are entire
Other conventional deformations and definition mode of ratio in configuration " also can satisfy chemical short parameter building of the invention, together
Sample should be included within protection scope of the present invention
2, the building of objective function
Chemical short parameter is introduced, the objective function of description scheme chemical short is constructed, which is used to retouch
State the short program of structure and the gap of restrictive condition.
Corresponding to above-mentioned rule a, the gap based on the chemical short parameter and restrictive condition:Construct the objective function are as follows:
Alternatively,
In above-mentioned formula (3), (4),Indicate the chemical short parameter alpha in configuration σj(ep,eq),
wj,p,qFor optional weight factor, WithThe respectively preset chemical short parameter alphaj(ep,eq) minimum value and maximum value.According to objective function
Form, be readily apparent that when objective function be 0 when, each subitem is 0, i.e.,
It should be noted that a series of short distance order parameters can be provided in modeling in the realization of SAE method.To appoint
It anticipates a kind of chemical short parameter restrictive condition, gives the target value of short distance order parameterDue to using one when modeling
A limited super born of the same parents of atom number, it cannot be guaranteed that the short distance order parameter of model built and target value strict conformance, so also to give
Short distance order parameter reserves certain surplus, therefore the previously given above-mentioned minimum value of short distance order parameterAnd maximum
Value
In addition, correspond to above-mentioned rule b, the gap based on the chemical short parameter and restrictive condition:Construct the objective function are as follows:
Alternatively,
In above-mentioned formula (7), (8),Indicate the chemical short parameter alpha in configuration σr(ep, eq),
wj,p,qFor optional weight factor, With
The respectively preset chemical short parameter alphar(ep, eq) minimum value and maximum value.According to the form of objective function, hold
Easily know that each subitem is 0, i.e., when objective function is 0
3, structure optimization stage by stage
The scheme of structure optimization stage by stage optimizes structural chemistry short program objective function, then the re-optimization degree of disorder first
Objective function requires in optimization process structure to meet the restrictive condition of chemical short.
A. the optimization of short program objective function
Above-mentioned objective function can be optimized by Metropolis Monte Carlo method, so that objective function
Value be gradually reduced, until close to 0.The following steps are included:
Step (1): random to generate configuration σ；
Step (2): for each chemical short parameter in objective function, the chemical short under configuration σ is calculated
The specific value of parameter；
Step (3): if all chemical short parameter values are all larger than equal to preset minimum value, and it is less than or equal to pre-
If maximum value, then terminate optimization to chemical short parameter；Otherwise, step (4) are executed；
Step (4): two symbol of element e in random exchange configuration σpAnd eqThe coordinate position of different atom obtains
One new configuration σ '；Calculate the objective function ε (σ) and ε (σ ') of configuration σ and configuration σ '；
Step (5): if ε (σ ') < ε (σ), returns to step (2) based on configuration σ '；Otherwise, it is with configuration σ
Basis returns to step (4).
When finding that configuration meets all short distance order parameters, the optimization to short distance order parameter can be terminated.
B. the optimization of degree of disorder objective function
Then, can continue with special quasi- random structure (SQS) method perhaps similar atomic environment (SAE) method or
The method of other description scheme longrange disorder degree optimize to the degree of disorder of structure.Referring to Fig. 1, to the degree of disorder into
While row optimization, using the short distance order parameter of configuration as restrictive condition, when the short distance order parameter of configuration σ meets given limitation
When condition, just using configuration σ as the candidate structure in degree of disorder optimization process.For meeting the structure of short distance order parameter, then into
The calculating of row degree of disorder parameter, optimizes the degree of disorder.
By the strategy of hierarchy optimization above, the first step optimizes short program objective function, meets structure
Short program limitation；Second step, under conditions of keeping short program limitation, with SQS method or SAE method or other methods pair
The degree of disorder optimizes.Optimize by this two step, can obtain in the case where meeting short program Parameter Conditions closest to unordered solid solution
Body structure.
The above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are not by above-described embodiment
Limitation, other any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present invention,
It should be equivalent substitute mode, be included within the scope of the present invention.
Claims (9)
1. a kind of unordered solid-solution material modeling method, it is characterised in that: the target of this method introducing description scheme short program situation
Function, the objective function are constructed based on chemical short parameter, and the chemical short parameter is based on: in unordered solid-solution material
It models in configuration, the first Elements Atom of distance meets the ratio of the second element atom at a preset positional relationship, Yi Ji
Ratio of the Was Used atom in entire configuration and construct.
2. modeling method according to claim 1, it is characterised in that: the chemical short parameter is αj(ep,eq), it is full
Sufficient formula (1) or formula (2):
Wherein, Pj(ep,eq) be for all elements symbol be epAtom jth neighbour's atom in, symbol of element eqOriginal
The ratio of son, cqFor e in entire configurationqThe ratio of Elements Atom；
Wherein, P 'j(ep, eq) be for all elements symbol be epAtom, from the 1st neighbour into all atoms of jth neighbour,
The symbol of element is eqAtom ratio, cqFor e in entire configurationqThe ratio of Elements Atom.
3. modeling method according to claim 2, it is characterised in that: be based on the chemical short parameter and restrictive condition
Gap:Construct the objective function；
Wherein,Indicate the chemical short parameter alpha in configuration σj(ep,eq)；
Wherein, WithIt is respectively preset
The chemical short parameter alphaj(ep,eq) minimum value and maximum value.
4. modeling method according to claim 3, it is characterised in that: the objective function are as follows:
Alternatively,
In above-mentioned formula (3), (4),Indicate the chemical short parameter alpha in configuration σj(ep,eq), wj,p,qFor
Optional weight factor.
5. modeling method according to claim 1, it is characterised in that: the chemical short parameter is αr(ep, eq), it is full
Sufficient formula (5) or formula (6):
Wherein, Pr(ep,eq) be for the symbol of element be epAll atoms, with these atomic distances be r atom in, element
Symbol is eqAtom shared by ratio, cqFor e in entire configurationqThe ratio of Elements Atom；
Wherein, P 'r(ep, eq) indicate to be e for the symbol of elementpAll atoms, with these atomic distances be less than r all originals
In son, symbol of element eqAtom shared by ratio, cqFor e in entire configurationqThe ratio of Elements Atom.
6. modeling method according to claim 5, it is characterised in that: be based on the chemical short parameter and restrictive condition
Gap:Construct the objective function；
Wherein,Indicate the chemical short parameter alpha in configuration σr(ep, eq)；
Wherein, WithIt is respectively preset
The chemical short parameter alphar(ep, eq) minimum value and maximum value.
7. modeling method according to claim 6, it is characterised in that: the objective function are as follows:
Alternatively,
In above-mentioned formula (7), (8),Indicate the chemical short parameter alpha in configuration σr(ep, eq), wj,p,qFor
Optional weight factor.
8. according to the modeling method any in claim 3,4,6,7, it is characterised in that: further include to objective function and change
The step of learning short program parameter optimization:
Step (1): random to generate configuration σ；
Step (2): being directed to all chemical short parameters relevant to objective function, calculates the chemical short under configuration σ
The specific value of parameter；
Step (3): if all chemical short parameter values are all larger than equal to preset minimum value, and it is less than or equal to preset
Maximum value then terminates the optimization to chemical short parameter；Otherwise, step (4) are executed；
Step (4): two symbol of element e in random exchange configuration σpAnd eqThe coordinate position of different atom obtains one
New configuration σ '；Calculate the objective function ε (σ) and ε (σ ') of configuration σ and configuration σ '；
Step (5): if ε (σ ') < ε (σ), returns to step (2) based on configuration σ '；Otherwise, based on configuration σ
Return to step (4).
9. modeling method according to claim 8, it is characterised in that: big to above-mentioned all chemical short parameter values
In being equal to preset minimum value, and it is less than or equal to configuration corresponding to preset maximum value, further executes degree of disorder parameter
It calculates and optimizes；The calculating of the degree of disorder parameter and optimization based on SQS method perhaps SAE method or other can describe
The method of structure longrange disorder feature.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20120109966A1 (en) * | 2010-11-01 | 2012-05-03 | Jisheng Liang | Category-based content recommendation |
| US8315353B1 (en) * | 2010-03-17 | 2012-11-20 | General Electric Company | System and method of prior image constrained image reconstruction using short scan image data and objective function minimization |
| CN104361181A (en) * | 2014-11-20 | 2015-02-18 | 集美大学 | Implementing method of dual alloy nanoparticle catalyst stable structure |
| CN107391855A (en) * | 2017-07-26 | 2017-11-24 | 华中科技大学 | A kind of material structure integration construction method towards a variety of microstructures |
| CN108256288A (en) * | 2018-01-18 | 2018-07-06 | 安徽工业大学 | A kind of method of Local Structure in identification non-crystaline amorphous metal |
-
2019
- 2019-03-01 CN CN201910154739.0A patent/CN110033833B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8315353B1 (en) * | 2010-03-17 | 2012-11-20 | General Electric Company | System and method of prior image constrained image reconstruction using short scan image data and objective function minimization |
| US20120109966A1 (en) * | 2010-11-01 | 2012-05-03 | Jisheng Liang | Category-based content recommendation |
| CN104361181A (en) * | 2014-11-20 | 2015-02-18 | 集美大学 | Implementing method of dual alloy nanoparticle catalyst stable structure |
| CN107391855A (en) * | 2017-07-26 | 2017-11-24 | 华中科技大学 | A kind of material structure integration construction method towards a variety of microstructures |
| CN108256288A (en) * | 2018-01-18 | 2018-07-06 | 安徽工业大学 | A kind of method of Local Structure in identification non-crystaline amorphous metal |
Non-Patent Citations (2)
| Title |
|---|
| FUYANG TIAN等: ""A structural modeling approach to the solid-solution materials"", 《ARXIV.ORG,ARXIV:1810.06144》 * |
| 莫云飞: ""液态金属铜及铜锆合金快速凝固过程中相转变微观机理的模拟研究"", 《中国博士学位论文全文数据库 工程科技丨辑》 * |
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