P H Y S electronic Structure Calculations for Cr 1 - xAlx CNF Project Number : 1845 - 09 Principal Investigator :

Cr3Al shows semiconductor-like behavior, attributed to a combination of antiferromagnetism and chemical ordering. We present a detailed study of chemical ordering in Cr3Al. Using density functional theory within the Korringa Kohn Rostoker (KKR) formalism, we consider five possible Cr3Al structures. The chemically ordered, rhombohedrally distorted X-phase has the lowest energy and should therefore be the ground state found in nature. The D03 structure has the highest energy and should not occur. While KKR indicates a pseudogap in the X-phase density of states, calculations using full potential linear muffin tin orbital and plane wave techniques show a narrow band gap. Summary of Research: The nature of a gap in Cr3Al is currently of interest. Experimental results in the literature are suggestive of either a semimetal or degenerate semiconductor [1]. A full gap might suggest further study of Cr3Al as a potential thermoelectric material [2]. In addition, recent theoretical work has predicted that Cr3Al with binary Heusler (D03) ordering is almost completely spin polarized and that Mn-doped D03 Cr3Al would behave as a true half metal with applications in spintronics [3]. While no evidence of D03 ordering has been shown in Cr3Al, the Cr-Al phase diagram is not well established [4]. Thus, a study of the nature of a gap in Cr3Al and how it is affected by chemical ordering is warranted. We will explore here the three structures shown on the proposed phase diagram for Cr3Al: bcc solid solution, C11b Cr2Al + bcc Cr two-phase system, and X-phase Cr3Al structure [4]. Also included are an off-stoichiometric C11b Cr3Al structure, seen Figure 1: Structures considered. experimentally for films grown at 500-600°C [5] and the D03 (Heusler) structure. These structures are shown in Figure 1. DFT calculations were done on the Intel cluster at the Cornell NanoScale Facility. All structures were evaluated using the AkaiKKR code, so the results for the different structures could be compared directly. This technique was chosen for its ability to treat site disorder, which was necessary for the bcc solid solution and off-stoichiometric C11b Cr3Al structures. Disorder is treated using the coherent potential approximation (CPA) [6]. The total energy per atom is shown in Table 1. The X-phase structure has the lowest energy, suggesting that it is the low temperature stable phase for the Cr3Al stoichiometry, confirming the proposed phase diagram [4]. PHYSICS & NANOSTRUCTURE PHYSICS 233 2011-2012 CNF RESEARCH ACCOMPLISHMENTS P H Y S The bcc solid solution, C11b Cr2Al + bcc Cr two phase system, and C11b Cr3Al structure have the next lowest energies, consistent with their being stable phases at higher temperatures. Finally, the D03 structure has a significantly higher energy. The table also shows the density of states (DOS) at EF. The lowest DOS(EF), as calculated by KKR, occurs for X-phase Cr3Al due to barely overlapping bands at EF [5]. DFT calculations often underestimate the band gap in materials, sometimes showing overlapping bands in materials known to have a full band gap. Therefore, to complement the KKR calculations, we performed calculations using a plane wave approach (Quantum Espresso) and a full potential linear muffin tin orbital approach (FP-LMTO) [7, 8]. Figure 2 compares the calculated DOS for the three approaches. It is clear that, overall, the approaches produce similar features in the DOS near EF. Quantum Espresso predicts a small but complete gap of 200 meV and FP-LMTO predicts a smaller gap of 40 meV. Thus, the semiconductor-like behavior in Cr3Al can be explained by X-phase ordering leading to a gap in the DOS. It is likely that a perfect crystal of X-phase Cr3Al would be a true narrow-gap semiconductor with a band gap greater than 40 meV. However, real samples thus far show the X-phase occurring in very small domains presumably separated by antiphase boundaries [9]. Disorder could smear the band edges or introduce defect states. The experimental observations of Cr3Al are consistent with a small but finite DOS(EF) [1]. A band gap can only occur in a material with an even number of valence electrons per unit cell in order to completely fill the valence band. So how can Cr3Al, with 21 electrons per Table 1: Total energy (relative to minimum energy structure) and DOS(EF) for the five Cr3Al structures. Figure 2: The density of states for X-phase Cr3Al calculated using the three approaches. formula unit, have a band gap? The gap is possible because the primitive unit cell of the X-phase, shown in Figure 1, is actually Cr6Al2, having 42 valence electrons per unit cell. This aspect of the X-phase structure sets it apart from the other structures, which, although they may have a low DOS(EF), have an odd number of valence electrons per unit cell and therefore must have partially filled bands crossing EF. This study of the chemical ordering of Cr3Al has important implications for materials design of transition metal compounds. The energy calculations indicate the D03 structure should not occur under equilibrium conditions. This may represent a lower limit on the number of valence electrons in the unit cell for the Heusler structure. Heusler alloys are usually studied with 22-31 valence electrons in the formula unit, while Cr3Al has 21 [10]. Similar compounds containing transition metals from the left side of the periodic table should be studied for X-phase type ordering.