Efficient Search Algorithm For The Structures Of Site-occupancy Disorder

In condensed-matter physics,the structure-property relationships of materials are the key to the design and optimization of n ovel functional materials,while deciphering the microstructures of materials is an essential prerequisite to uncover its structureproperty relationships.The system of site-occupancy disorder,represented by random multicomponent alloys(e.g.,high-entropy alloys),shows great natural advantages in the design of unique properties of materials because of its near-infinite configuration space.Unfortunately,however,the structure search in the systems of site-occupancy disorder got stuck due to the insurmountable challenge caused by combinatorial explosion,i.e.,the number of site-occupancy configurations grows explosively with the increase of atoms and components.Try to overcome the difficulty of combinatorial explosion to speed up the structure search in the system of site-occupancy disorder will greatly promote its exploration in structure-property relationships.Starting from the perspective of physics and algorithm,in this dissertation,a highly efficient search algorithm for irreducible site-occupancy configurations and strategy for special quasirandom structures are designed.Searching irreducible(i.e.geometrically inequivalent)site-occupancy configurations in the whole configuration space is one of the vital means to partially avoid combinatorial explosion.Based on the space group symmetry of the underlying lattice and the basic theory of combinatorics,an efficient search algorithm for irreducible site-occupancy configurations is proposed,which is suitable for any underlying lattice with arbitrarily supercell shape,and any number of components with arbitrarily atomic composition.The algorithm searches the space group operation of the supercell through its structural information(including lattice vectors and atomic coordinates),and constructs the equivalent atomic matrix based on it,so that the equivalent configurations can be identified quickly.To efficiently eliminate the equivalent configurations,continuous integers is used to represent each configuration,and the fast conversion formulas from any configuration(integer)to the corresponding integer(configuration)is derived,which greatly improves the efficiency of the algorithm and realizes the time complexity of O(N),i.e.,the run time of the algorithm scales linearly with the number of i rreducible site-occupancy configurations.Although the efficiency of the above algorithm in the binary site-occupancy systems exceeds the related existing algorithms,it does not achieve the expected efficiency in the multinary(more than binary)site-occupancy systems owing to its deficiency in algorithm framework.Therefore,on the basis of maintaining the kernel of the original algorithm,by abstracting the search of irreducible site-occupancy configurations into a tree-like structure and block the branches of the tree that do not meet the requirements,a tree search algorithm for irreducible site-occupancy configurations is proposed.The efficiency(especially for the multinary site-occupancy systems)of our tree search algorithm is far beyond(about 1～2 orders of magnitude higher)that of the original algorithm and related existing algorithms,as it avoids the combinatorial explosion to a greater extent.The proposed tree search algorithm for irreducible site-occupancy configurations is efficient and universal,so it can be effectively used for the structure search in various systems of site-occupancy disorder,and provide strong support for the relevant modeling methods,such as special quasirandom structure(SQS)and small set of ordered structures,of disordered alloys.When trying to search the SQS of multicomponent alloys by using the tree search algorithm,although the optimal SQS for ternary equiatomic body-centered cubic(bcc)and face-centered cubic(fcc)alloys have been successfully searched out,the time required for higher-component alloys is far beyond the reasonable limit.Therefore,based on the tree search algorithm,an extremely efficient configuration decomposition technique is proposed to search the optimal SQS for multicomponent alloys.The key concept of configuration decomposition is to decompose the configuration of a multinary alloy into several subconfigurations of binary alloy s,and it can be inferred that if a configuration is the SQS of a multinary alloy,i ts subconfigurations must be the SQS of their corresponding binary alloy.Compared with traditional exhaustive method,the efficiency of configuration decomposition technique is improved by several orders of magnitude;taking ternary(quaternary)bcc and fcc alloys as examples,their efficiency has increased by about four(seven)orders of magnitude,while for higher-component alloys,their efficiency will be improved more significantly.In addition,the searched SQS based on configuration decomposition technique is far superior to that obtained by Monte Carlo simulated annealing technique,so it can be widely used as a standard SQS in the study of various alloy properties.