Chemical ordering in Cr${}_3$Al and relation to semiconducting behavior

Cr${}_3$Al shows semiconductor-like behavior which has been attributed to a combination of antiferromagnetism and chemical ordering of the Cr and Al atoms on the bcc sublattice. This article presents a detailed theoretical and experimental study of the chemical ordering in Cr${}_3$Al. Using density functional theory within the Korringa-Kohn-Rostoker (KKR) formalism, we consider five possible structures with the Cr${}_3$Al stoichiometry: a bcc solid solution, two-phase C11${}_b$ ${\mathrm{Cr}}_2\mathrm{Al}+\mathrm{Cr}$, off-stoichiometric C11${}_b$ Cr${}_3$Al, D0${}_3$ Cr${}_3$Al, and X-phase Cr${}_3$Al. The calculations show that the chemically ordered, rhombohedrally distorted X-phase structure has the lowest energy of those considered and should, therefore, be the ground state found in nature, while the D0${}_3$ structure has the highest energy and should not occur. While KKR calculations of the X phase indicate a pseudogap in the density of states, additional calculations using a full potential linear muffin-tin orbital approach and a plane-wave technique show a narrow band gap. Experimentally, thin films of Cr${}_{1-x}$Al${}_x$ were grown and the concentration, growth temperature, and substrate were varied systematically. The peak resistivity (2400 $\mu \Omega$-cm) is found for films with $x=0.25$, grown epitaxially on a 300 ${}^{\circ }$C MgO substrate. At this $x$, a transition between nonmetallic and metallic behavior occurs at a growth temperature of about 400 ${}^{\circ }$C, which is accompanied by a change in chemical ordering from X phase to C11${}_b$ Cr${}_3$Al. These results clarify the range of possible structures for Cr${}_3$Al and the relationship between chemical ordering and electronic transport behavior.

Figure 1

Binary phase diagrams of the Cr${}_{1-x}$Al${}_x$ system, as shown by Koster et al.[10, 50] and Murray.[15, 51] (Adapted with the permission of ASM International. All rights reserved. www.asminternational.org.)

Figure 2

Structures considered in Secs. 5 and 6. (b) In the bcc solid solution, the atoms are randomly Cr or Al in the ratio Cr${}_{0.75}$Al${}_{0.25}$. (d) In the off-stoichiometric C11${}_b$ Cr${}_3$Al phase, the atoms at the Al sites are randomly Cr or Al in the ratio Cr${}_{0.25}$Al${}_{0.75}$, for a total stoichiometry of Cr${}_2$(Al${}_{0.75}$Cr${}_{0.25}$), or Cr${}_3$Al.

Figure 3

XRD of epitaxial Cr${}_{0.76}$Al${}_{0.24}$ (a) $\theta -2\theta$ survey of films grown at 300 ${}^{\circ }$C. (b) (0 0 $\frac{2}{3}$) peak of films grown at several temperatures. (c) (0 0 2) peak of films for several growth temperatures. Note that some of the (002) peaks have sufficient intensity to show thickness oscillations, corresponding to the approximately 400-Å thickness of the films.

Figure 4

Resistivity of Cr${}_{1-x}$Al${}_x$ thin films vs $x$ at 2 K. All films shown here were grown at 300 ${}^{\circ }$C. Bulk data from Ref. 6. Error bars are smaller than the symbol size. Inset: Resistivity of Cr${}_{0.77}$Al${}_{0.23}$ vs temperature.

Figure 5

The 2 K resistivity of Cr${}_{0.76}$Al${}_{0.24}$ thin films vs growth temperature. Error bars are smaller than the symbol size. The X-phase boundary at 400 ${}^{\circ }$C was proposed by den Broeder et al. in Ref. 14.

Figure 6

Band structure of Cr and X-phase Cr${}_3$Al, for nonmagnetic and antiferromagnetic cases, calculated using the AkaiKKR technique. (a) Nonmagnetic Cr in the cubic Brillouin zone. (b) Nonmagnetic Cr, (c) antiferromagnetic Cr, (d) nonmagnetic X-phase Cr${}_3$Al, and (e) antiferromagnetic X-phase Cr${}_3$Al, all in the rhombohedral Brillouin zone. (f) Cubic and rhombohedral zones and symmetry points. For reference, point $T$ occurs along the bcc [111] axis (the long axis of the rhomboid unit cell in real space).

Figure 7

Total density of states for the X phase of Cr${}_3$Al as calculated using the FP-LMTO approach [solid (black) line], plane-wave pseudopotential approach [dash-dotted(red) line], and KKR technique [filled (black) squares]. The energy 0 is set to the Fermi energy in all cases.