Multi-Objective Optimization as a Tool for Material Design

Nonempirical Definition of the Mendeleev Numbers: Organizing the Chemical Space

“…Of these, only 446 systems have the magnetic information that are obtained in several multi-objective evolutionary searches for low-energy and highly magnetized phases, as implemented in the USPEX algorithm. 15 The hardness of all crystal structures in this database was computed using the Lyakhov-Oganov model. 16 The database is fully consistent because all crystal structures were relaxed and their energies computed in the same settings using the density functional theory with the projector-augmented wave method (PAW) and PBE 17 functional as implemented in the VASP code.…”

Coevolutionary search for optimal materials in the space of all possible compounds

“…Search for hard and superhard binary systems Pareto optimization 18 of hardness and stability was performed over all possible structures (with up to 12 atoms in the primitive cell) and compositions limited to the binary compounds of 74 elements (i.e., all elements excluding the noble gases, rare earth elements, and elements heavier than Pu). In this work, 600 systems have been computed in 20 MendS generations from a total of 2775 unary and binary systems that can be made of 74 elements, i.e., only about one fifth of all possible systems were sampled.…”

Computational Search for New W–Mo–B Compounds

“…A noteworthy feature of USPEX is the ability to predict crystal structures (unary, binary, ternary, etc.) that have not only a specific chemical composition but also desired physical properties by using multiobjective optimization …”

“…USPEX has been widely applied to the prediction of binary hard and superhard compounds (i.e., those with Vickers hardness > 40 GPa − ) such as metal borides, carbides, nitrides, and the like. − ,− Apart from their high hardness, these materials are also known for a combination of outstanding physical properties: electrical conductivity, low compressibility, high melting temperature, and high shear strength. − Some physical properties of binary compounds, such as hardness for metal borides, could be further improved by adding a third element: an addition of 3 atom % of Mo to “WB 4 ” (now it is established that this phase is WB 5– x with typical x ∼ 0.7–0.8) leads to a 15% increase in Vickers hardness, from 28.1 ± 1.4 to 33.4 ± 0.9 GPa when the applied load is 4.90 N. , Furthermore, varying the W:Mo ratio may lead to the formation of new ternary structures, with unknown structural motifs and with mechanical properties exceeding those of the pristine and doped binary compounds. Thus, the prediction of the crystal structure of ternary compounds becomes fundamentally important for new hard and superhard materials.…”

“…that have not only a specific chemical composition but also desired physical properties by using multiobjective optimization. 9 USPEX has been widely applied to the prediction of binary hard and superhard compounds (i.e., those with Vickers hardness > 40 GPa 5−7 ) such as metal borides, carbides, nitrides, and the like. 8−22,28−32 Apart from their high hardness, these materials are also known for a combination of outstanding physical properties: electrical conductivity, low compressibility, high melting temperature, and high shear strength.…”