Research ArticleMATERIALS SCIENCE

Prediction and synthesis of a family of atomic laminate phases with Kagomé-like and in-plane chemical ordering

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Science Advances  19 Jul 2017:
Vol. 3, no. 7, e1700642
DOI: 10.1126/sciadv.1700642
  • Fig. 1 Measured and simulated XRD of atomic laminate phases with in-plane chemical ordering.

    (A and C) Measured XRD data for (V2/3Zr1/3)2AlC and (Mo2/3Y1/3)2AlC i-MAX phases and (B and D) corresponding simulated patterns. The simulations are based on structures with monoclinic C2/c symmetry being relaxed with GGA-PBEsol. The match between measured and calculated peaks is indexed by blue stars. The typical in-plane (110) peak of an i-MAX phase is indicated by an arrow.

  • Fig. 2 In-plane chemically ordered structure of (V2/3Zr1/3)2AlC.

    Structural confirmation of chemical ordering through HRSTEM images and corresponding schematic representation of (V2/3Zr1/3)2AlC. (A) Structure overview along the [010] axis and (B) along the [103] zone axis. From the enlarged HRSTEM images along the (C) [010], (D) [110], and (E) [100] zone axis, with corresponding SAED in the inset, the in-plane chemical ordering is evident. Schematic representations are based on the atomic arrangements in a monoclinic structure of space group C2/c. The unit cell dimensions are represented with black lines in the schematics. Scale bars, 5 nm (A and B) and 2 nm (C to E).

  • Fig. 3 In-plane chemically ordered structure of (Mo2/3Y1/3)2AlC.

    Overview and enlarged HRSTEM, SAED, and schematic representation along (A) [110] and (B) [100] zone axis, respectively, based on a monoclinic structure of space group C2/c. The unit cell dimensions are represented with black lines in the schematics. Scale bar, 4 nm (1 nm for enlarged parts).

  • Fig. 4 Local atomic coordination in i-MAX phases.

    Exemplified by (V2/3Zr1/3)2AlC, the atomic surrounding is schematically illustrated for (A) V, (B) Zr, (C) Al, and (D) C seen from top view (top) and side view (bottom). Note that the local atomic coordination is the same for the four candidate structures evaluated here.

  • Fig. 5 Overview of atomic structure in MAX versus i-MAX and comparison of ideal Kagomé and Kagomé-like lattices.

    Comparison between the MAX phase structure (top) and i-MAX structure with in-plane chemical order (center) assuming a (V2/3Zr1/3)2AlC composition. (A) M layer composed of V and Zr, (B) Al layer, (C) C layer. (D) Top view of C-M-Al-M-C block, and (E) side view of C-M-Al-M-C block. Schematic of Al atoms arranged in (F), an ideal Kagomé lattice and (G) a Kagomé-like lattice as found in i-MAX phases. Note slight ripple in atom locations in (G). To illustrate the deviation in atom positions, both (F) and (G) are superimposed in (H), with arrows indicating their undulations. We also show that the angle, θ, along the atomic “chains,” which for an ideal Kagomé lattice, is always 180°, whereas for the Kagomé-like lattice in an i-MAX phase, there is a small deviation. In addition, we estimate the displacement of Al away from its ideal positions, Δd1 and Δd2.

  • Table 1 Predicted and verified compounds.

    Calculated stability and experimental observations for (V2/3Zr1/3)2AlC and (Mo2/3Y1/3)2AlC as well as the hypothetical (Zr2/3V1/3)2AlC and (Y2/3Mo1/3)2AlC.

    Targeted ordered phaseΔHcp (meV per atom)Equilibrium simplex*Experimental observation
    (V2/3Zr1/3)2AlC−50V2AlC, Zr4AlC3, Zr2Al3, V2CYes
    (Zr2/3V1/3)2AlC+40Zr4AlC3, Zr2Al3, V2C, V2AlCNo
    (Mo2/3Y1/3)2AlC−101YMoC2, Mo3Al, YAl2, YAl3C3Yes
    (Y2/3Mo1/3)2AlC+13YAl2, Mo3Al, Y4C5, Y3AlCNo

    *For each phase, we present the identified equilibrium simplex (set of most competing phases).

    • Table 2 Calculated crystallographic data for monoclinic C2/c (V2/3Zr1/3)2AlC and (Mo2/3Y1/3)2AlC structures.

      Structural relaxation performed using GGA-PBEsol exchange-correlation functional.

      CompoundLattice parameters (Å, degrees)AtomWyckoff siteAtomic coordinates (fractional)
      (V2/3Zr1/3)2AlCa = 9.1720b = 5.2808c = 13.6416Zr18f−0.042240.419650.11240
      α = 90.0000β = 103.0708γ = 90.0000V18f0.271000.421630.07627
      V28f0.609220.406780.07628
      Al14e0.00000−0.071570.25000
      Al28f0.744320.159030.25156
      C14d0.250000.250000.50000
      C28f0.414010.25792−0.00009
      (Mo2/3Y1/3)2AlCa = 9.5764b = 5.5433c = 14.1582Y18f−0.039240.419280.11779
      α = 90.0000β = 103.6620γ = 90.0000Mo18f0.270640.423560.07656
      Mo28f0.609980.403890.07660
      Al14e0.00000−0.080270.25000
      Al28f0.748180.160620.25156
      C14d0.250000.250000.50000
      C28f0.412850.260730.00003
    • Table 3 Impact of atomic size on formation of chemically ordered structures.

      Energy difference, ΔE, between the chemically ordered i-MAX phase and the related MAX phase with a disordered distribution of M 1 and M 2 on the M lattice, for (V2/3Zr1/3)2AlC, (Mo2/3Y1/3)2AlC, (Mo2/3Sc1/3)2AlC, and the hypothetical (V2/3Ti1/3)2AlC. The corresponding temperature, Tdisorder, required for decreasing the free energy of the disordered phase to the ordered one through the entropic contribution to Gibbs free energy. The difference in the atomic radius (metallic) and electronegativity between the two metals M1 and M2 is also included.

      M1M2ΔE (meV per
      atom)
      Tdisorder
      (K)
      Difference between M2 and M1
      Atomic
      radius* (Å)
      Electronegativity
      VZr−13649510.25−0.30
      MoY−19771920.41−0.94
      MoSc−8229990.23−0.80
      VTi−124380.12−0.09

      *1.35 Å for V, 1.60 Å for Zr, 1.39 Å for Mo, 1.80 Å for Y, 1.62 Å for Sc, and 1.47 Å for Ti.

      †1.63 Å for V, 1.33 Å for Zr, 2.16 Å for Mo, 1.22 Å for Y, 1.36 Å for Sc, and 1.54 Å for Ti

      Supplementary Materials

      • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/7/e1700642/DC1

        section S1. Dynamical stability

        section S2. Elemental mapping

        section S3. Candidate structures

        section S4. Impact of atomic size

        section S5. Cell size convergence for disordered structures

        section S6. Competing phases used for stability calculations

        fig. S1. Dynamical stability of ordered structures.

        fig. S2. Elemental mapping of (Mo2/3Y1/3)2AlC.

        fig. S3. Comparison of different in-plane chemically ordered candidate structures.

        fig. S4. Calculated energy and structural changes upon metal displacement.

        fig. S5. Structural changes upon metal displacement.

        fig. S6. Ratio of two Al-Al distances upon metal displacement.

        fig. S7. Energy change upon metal displacement.

        fig. S8. Supercell convergence.

        table S1. Energy degeneracy of candidate structures.

        table S2. Calculated crystallographic data for different candidate structures of (V2/3Zr1/3)2AlC.

        table S3. Calculated crystallographic data for different candidate structures of (Mo2/3Y1/3)2AlC.

        table S4. Calculated crystallographic data for different candidate structures of (V2/3Zr1/3)2AlC using the LDA exchange-correlation functional.

        table S5. Calculated crystallographic data for different candidate structures of (Mo2/3Y1/3)2AlC using the LDA exchange-correlation functional.

        table S6. Calculated crystallographic data for different candidate structures of (V2/3Zr1/3)2AlC using the GGA-PBEsol exchange-correlation functional.

        table S7. Calculated crystallographic data for different candidate structures of (Mo2/3Y1/3)2AlC using the GGA-PBEsol exchange-correlation functional.

        table S8. Phases considered for the quaternary Mo-Y-Al-C system.

        table S9. Phases considered for the quaternary V-Zr-Al-C system.

      • Supplementary Materials

        This PDF file includes:

        • section S1. Dynamical stability
        • section S2. Elemental mapping
        • section S3. Candidate structures
        • section S4. Impact of atomic size
        • section S5. Cell size convergence for disordered structures
        • section S6. Competing phases used for stability calculations
        • fig. S1. Dynamical stability of ordered structures.
        • fig. S2. Elemental mapping of (Mo2/3Y1/3)2AlC.
        • fig. S3. Comparison of different in-plane chemically ordered candidate structures.
        • fig. S4. Calculated energy and structural changes upon metal displacement.
        • fig. S5. Structural changes upon metal displacement.
        • fig. S6. Ratio of two Al-Al distances upon metal displacement.
        • fig. S7. Energy change upon metal displacement.
        • fig. S8. Supercell convergence.
        • table S1. Energy degeneracy of candidate structures.
        • table S2. Calculated crystallographic data for different candidate structures of (V2/3Zr1/3)2AlC.
        • table S3. Calculated crystallographic data for different candidate structures of (Mo2/3Y1/3)2AlC.
        • table S4. Calculated crystallographic data for different candidate structures of (V2/3Zr1/3)2AlC using the LDA exchange-correlation functional.
        • table S5. Calculated crystallographic data for different candidate structures of (Mo2/3Y1/3)2AlC using the LDA exchange-correlation functional.
        • table S6. Calculated crystallographic data for different candidate structures of (V2/3Zr1/3)2AlC using the GGA-PBEsol exchange-correlation functional.
        • table S7. Calculated crystallographic data for different candidate structures of (Mo2/3Y1/3)2AlC using the GGA-PBEsol exchange-correlation functional.
        • table S8. Phases considered for the quaternary Mo-Y-Al-C system.
        • table S9. Phases considered for the quaternary V-Zr-Al-C system.

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