Irradiation Resistance of Multicomponent Alloys
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I.
INTRODUCTION
TYPICAL metallic alloys used in industrial applications contain one principal constituent element and many additions of other elements. In contrast highentropy alloys (HEAs)[1–3] have nearly equal contents of various elements to maximize the compositional entropy. The idea is that the high compositional entropy stabilizes a solid solution, preventing decomposition into multiple phases during casting. Mixing of various elements, however, brings about another conspicuous characteristic as a byproduct, namely high atomic-level stresses.[4,5] Elements with different atomic sizes occupying the same lattice site invariably produce local stresses at the atomic level. In this article, we focus on the atomic-level stresses in multicomponent alloys, and discuss possible consequences on resistance against irradiation damage. II.
ATOMIC SIZE EFFECT IN HEA
Stresses are usually defined for a continuum body. We consider affine deformation; r0 ¼ ð1 þ eÞr;
½1
T. EGAMI, Professor, is with the Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, and also with the Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, and Oak Ridge National Laboratory, Oak Ridge, TN 37831. Contact e-mail: [email protected] W. GUO, Graduate Student, is with the Department of Materials Science and Engineering, University of Tennessee. P.D. RACK, Professor, is with the Department of Materials Science and Engineering, University of Tennessee, and also with the Oak Ridge National Laboratory. T. NAGASE, Associate Professor, is with the Research Center for Ultra-High Voltage Electron Microscopy, Osaka University, Ibaraki, Osaka 567-0047, Japan, and also with the Division of Materials and Manufacturing Science, Graduate School of Engineering, Osaka University, Suita, Osaka 565-0871, Japan. Manuscript submitted May 1, 2013. METALLURGICAL AND MATERIALS TRANSACTIONS A
where r and r¢ are the positions before and after deformation, and e is the strain tensor. We then consider the change in energy of the solid due to deformation, V E eab ¼ Eð0Þ þ Vrab eab þ Cabcd eab ecd þ . . . 2
½2
where V is the volume, rab is the stress, Cabcd is the elastic constant, and a and b are Cartesian coordinates.[6] We can extend this formulation to the definition of the atomic-level stresses by dividing the energy into local energies for the cell which contains one atom; X Ei ; ½3 E¼ i
and considering the local responses to the affine strain.[4,7] For a system that can be described in terms of two-body forces, the stress is given by 1X a b rab f r ; ½4 i ¼ Vi j ij ij where Vi is the local atomic volume, and faij and rbij are the a and b components of the force and separation between atoms i and j. The stress tensor can be expressed in terms of a pressure, pi, and five shear stresses, sm,i.[4,7] If one alloys an element B with the atomic radius rB into a crystal of A element with the atomic radius rA, the element B will be under pressure because of the size difference. We found out recently that
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