Ab-initio tiling and atomic structure for decagonal ZnMgY quasicrystal

Abstract

We discover the detailed atomic structure of -MgZnY, a stable decagonal quasicrystal alloy of the layered Frank–Kasper type, and related phases, using the ‘tiling and decoration’ approach. The atoms have invariable sites in the rectangle and triangle tiles of a 10-fold-symmetric planar tiling. To discover the lowest-energy structures, we combine the methods of density functional theory (DFT) total energy calculations, empirical oscillating pair potentials (fitted to DFT), fitting effective Hamiltonians for tilings, and discovering optimum tiling structures using a nonlocal tile-reshuffling algorithm. We find a family of almost stable binary compounds with varying composition, including the decagonal quasicrystal and the known MgZn; in addition, we show the ternary versions can be stable: -MgZnY at high temperature, and -MgZnSc even at .

Keywords:

• Frank–Kasper
• effective Hamiltonian
• Mg–Zn–Y
• rectangle-triangle tiling
• ab-initio energies

Notes

1 The phase has been recently reported in the ternary AlMgZn system, at Al content of just 3% [19]).

2 We studied Mg51Zn20 at four Zn/Mg compositions: 17/54, 18/53, 19/52 and 20/51. Only 17/54 was stable at T = 0 K, other compositions were unstable by  1.5meV/atom.

3 This conclusion is wholly consistent with the recently obtained image of -MgZnDy, obtained by high-angle annular dark-field electron microscopy (HAADF) in Ref. [12]. When a hexagon-rhombus tiling is drawn over this image, similar to Figure 3(e), the bright spots indicating Dy atoms fall in the tips of rhombi corresponding to exactly these triangles.

4 A systematic study was done only using PAW-GGA potentials, according to which the cost was 210–270 meV on these sites.

5 It should be noted that these results are very senstive to the values of and ; when they were computed using the older PAW-GGA potential, was half as big and was twice as big, which predicts stability beginning at about twice the temperature and at smaller content of Y.

MM, CLH, and J. R-D. were supported by U.S. Department of Energy [grant number DE-FG02-89ER-45405]. MM was also supported by Slovak national grants [grant numbers: VEGA j2/0111/11; APVV-0647-10; APVV-0492-11].