D. Al-Cu bond shortening and electronic structure
In this section we discuss possible origins of the Al-Cu bond shortening. The
bond shortening is observed not only in our EAM-MD results, but also in our ab initio
simulation. For the ab initio MD-derived 200-atom MG, we can plot the charge density
distribution, as shown below in Fig. S14. The unusual density distribution between Al-Cu
bonds suggests electronic interaction between Al and Cu may be different from other
pairs.
Figure S14. Charge density distribution in Cu46Zr47Al7. Black circle highlights charge
distribution between Al-Cu bonds. The 200-atom configuration was obtained using ab
initio MD quenching (the one in Fig. S10b). The unit of charge density is NVE/Å3, i.e.
number of valence electron per Å3. Note that in VASP (PAW), the total number of
valence electrons is 11 for Cu, 4 for Zr, and 3 for Al.
However, the raw charge density alone may not be sufficiently informative and
revealing. We therefore studied the projected electron density of states (DOS). To focus
1
on Al-Cu interaction in the MGs, we empolyed ab initio calculation on a Cu70Al10 (80
atoms) system. Here Cu-rich systems are investigated because Al atoms in Cu46Zr47Al7
are also embedded in a Cu-rich environment. Sample systems were first equilibrated at
2000 K for 1 ns, and then energy minimized to the local inherent structure (amorphous)
using VASP. Box sizes were adjusted to reach zero pressure of the inherent structures.
Due to the fluctuation induced by the small box size, multiple runs were conducted and
multiple configurations were calculated and analyzed, see below.
Figure S15. (a) Partial PDFs and (b) projected DOS of Cu70Al10. In panel (a), Al-Cu bond
shortening is confirmed by comparing the Al-Cu, Cu-Cu and Al-Al partial PDFs. Since
there are not enough Al atoms in the Cu-rich system, Al-Al partial PDF was obtained in
the Al-rich counterpart, i.e. Al70Cu10. All PDFs are averaged over 10 configurations to
eliminate noise. In panel (b), orbital-projected and site-projected DOS are plotted, with
the Wigner-Seitz radii of 1.402 Å (Al) and 1.312 Å (Cu) (default values of PAW). For
clarity, the high d peak of Cu was truncated in the middle. In the projected DOS, three
major features can be observed. ① Al s states are pushed down by the resonance effect
between Cu d band and Al s orbital, opening a pseudo-gap in the energy range of the Cu
d band [1]. ② Due to the strong interaction with Cu d states, Al p states are split into
bonding and antibonding parts, showing Fano-like shape in the projected DOS [2,3]. ③
The Al d states overlapping with Cu d band, as well as the similar profile of Al sp states
2
and Cu d states around Fermi level, are evidence of sp-d hybridization, i.e. the sp orbitals
in Al hybridize with d orbitals in Cu, forming hybridized spd states. These peaks with
similar profile are actually projected partials of the hybridized spd orbitals. All the above
features are results of coupling between the broad Al conduction band and the narrow
low-lying Cu d band, and our observations are corroborated by ab initio calculations on
various Cu-Al intermetallics [2,3].
Note that in the Al-Fe and Al-TM systems (Al-rich), sp-d hybridization has been
proposed to be the origin of bond shortening [4,5]. However, unlike Fe/Ni, Cu is a more
noble metal, with completely filled d shell for an isolated Cu atom, and nearly filled d
band for atoms in a metal or alloy [6]. The major part of d band is usually located around
4 eV below Fermi level. Therefore, hybridization with Cu d states is to be accompanied
by delocalization, which is consistent with the polarized charge density distribution
between Cu and Al in Fig. S14. On the other hand, due to the limited d states (per Cu
atom) that can be delocalized and hybridized with sp orbitals of Al, a Cu-rich
environment is important for a uniform shortening of Al-Cu bonds (hence the calculation
for a Cu-rich model above).
In summary, electronic interactions involving Al are bond-specific and
environment-specific, and the special features discussed above are potential stabilizing
factors and can be the reasons why Al-Cu bonds are shorter than a simple addition of
tabulated metallic radii.
References
1. G.T. de Laissardière and T. Fujiwara, Phys. Rev. B 50, 5999 (1994).
2. V. Fournée, E. Belin-Ferré, and J. Dubois, J. Phys.: Condens. Matter 10, 4231
(1998).
3. V. Fournée et al, Philo. Mag. B 79, 205 (1999).
4. H.Y. Hsieh et al., J. Mater. Res. 5, 2807 (1990).
5. K. Ahn, D. Louca, S.J. Poon, and G.J. Shiflet, Phys. Rev. B 70, 224103 (2004).
6. M. Widom, I. Al-Lehyani, and J.A. Moriarty, Phys. Rev. B 62, 3648 (2000).
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