High Entropy Alloys: Criteria for Stable Structure
- PDF / 948,896 Bytes
- 11 Pages / 593.972 x 792 pts Page_size
- 53 Downloads / 254 Views
tropy Alloys’ (HEA) represent a recent class of materials which constitute multiple principal elements in equiatomic or non-equiatomic proportions. The presence of a number of principal elements, particularly in equiatomic proportion, leads to a large configurational entropy and thus, high entropy of mixing. Consequently, these alloys tend to form solid solutions with simple crystal structures like FCC, BCC, or a mixture of both, rather than intermetallics or other complex phases.[1–4] A variety of HEAs have been explored till date and it has been reported that these alloys exhibit very promising properties like high strength, ductility, excellent fracture toughness at cryogenic temperatures (i.e., £ 77 K),[5] good resistance to wear, oxidation, and high temperature softening. These properties are directly related to the underlying crystal structure of the solid-solution phase. However, due to the absence of reliable information about the phase diagrams of multicomponent systems, the knowledge
SNEHASHISH TRIPATHY and SANDIP GHOSH CHOWDHURYare with the Materials Engineering Division, CSIRNational Metallurgical Laboratory, Jamshedpur, 831007, India. Contact e-mail: [email protected] GAURAV GUPTA is with the School of Materials Science & Technology, IIT BHU, Varanasi. Manuscript submitted June 5, 2017.
METALLURGICAL AND MATERIALS TRANSACTIONS A
about phase formation in such systems is restrictively dependent upon the experimental determination. Lately, in order to tackle this present limitation of classical thermodynamics-based phase prediction, there have been various attempts by researchers to lay down certain thumb rules for phase formation based upon first principle calculations, Calculation of Phase Diagram (CALPHAD) principles, as well as other thermodynamic and topological parametric approaches.[6–17] The existing phase prediction techniques range from the first principle-based DFT calculations to CALPHADbased Phase Diagram Evaluation techniques.[18–22] The first principle-based calculations are very much computationally intensive; however, these are the most efficient techniques when it comes to determination of ground-state crystal structure. These basically involve the solution of the Kohn–Sham formulation[23] which is a minimization procedure of a coupled set of Schrodinger Equations for each electron in the system; being solved individually, yet self-consistently for the electron density, q(r). The Kohn–Sham formulation is expressed as mentioned in Eq. [1], where the first term on the left represents kinetic energy of a single electron; the second term defines electron–ion coupling potential; the third term reflects the electron–electron interaction; and the fourth term is for the exchange correlation potential[18]: 2 Z h 2 qðr0 Þ r r þ Ve ðrÞ þ þ V dr ½ q ð r Þ Wi ðrÞ xc jr r0 j 2m ¼ i WiðrÞ ½1 The Kohn–Sham formulation assumes an initial crystal structure depending upon the symmetry of which the single-electron wave function is formulated in a plane wave basis. This is followed by the adoption
Data Loading...
