  Current definition of high-entropy alloys (HEAs) is commonly based on the
configurational entropy. But this definition depends only on the chemical
composition of a HEA and therefore cannot distinguish the information content
that is encoded in various local atomic arrangements and measurable by the
Shannon entropy in information theory. Here, inspired by the finding that
two-dimensional (2D) Sudoku matrices exhibit higher average Shannon entropy
than 2D random matrix counterparts, we propose high-Shannon-entropy alloys
(HSEA), whose structures are based on 3D Sudoku matrices. Despite the
constraints on the atomic arrangements to form a 3D Sudoku 4 x 4 x 4 matrix, we
find that, a prototypical HSEA, NbMoTaW has a lower energy than the same HEA
with a random structure due to the smaller lattice distortion. We compute the
electronic structures and mechanical properties and find that the HSEA exhibits
enhanced average Fermi velocity and ductility over the random NbMoTaW HEA.
Finally, we evaluate the formation energies of single vacancies and a vacancy
cluster in the HSEA, whose configurations mimic Sudoku puzzles with one and
several missing numbers, respectively. We find that a range of large energies
are required to generate such vacancies, which depend on the location and
species of missing atoms. Our work shows that introducing the Shannon entropy
to HEAs offers a useful metric to reveal more atomic details of HEAs and that
HSEAs represent an uncharted domain in the complicated energy landscape of HEAs
which may be endowed with improved properties.
