Synthesis, characterization and first principle modelling of the MAB phase solid solutions: (Mn_1-xCr_x)₂AlB₂ and (Mn_1-xCr_x)₃AlB₄

Figures & data

Figure 1. Crystal structures of, a) M₂AlB₂, b) M₃AlB₄, c) disordered (Mn_1-xCr_x)₂AlB₂, d) disordered (Mn_1-xCr_x)₃AlB₄ and e) ordered Mn₂CrAlB₄. Note that in the 212 structure (a), the layers stack along the b-direction, while in the 314 (b) they stack along the c-direction.

Figure 2. Calculated formation enthalpies, ΔH, at 0 K and Gibbs free energies of formation, ΔG, at T > 0 K for, a) (Mn_1-xCr_x)₂AlB₂ and, b) (Mn_1-xCr_x)₃AlB₄ solid solutions. In (a), enthalpies of ternaries, viz. −67 and −30 meV/atom for Mn₂AlB₂ and Cr₂AlB₂ respectively, are used as reference points (zero).

Table 1. Identified equilibrium simplex for (Mn_1-xCr_x)₂AlB₂ and (Mn_1-xCr_x)₃AlB₄ phases

x in (Mn1-xCrx)2AlB2	Equilibrium simplex	x in (Mn1-xCrx)3AlB4	Equilibrium simplex
0	Mn2AlB2	0	Mn2AlB2, MnB, MnB4
0.33	Mn2AlB2, Cr2AlB2	0.33	Mn2AlB2, CrB2
0.50	Mn2AlB2, Cr2AlB2
0.66	Cr2AlB2, Mn2AlB2	0.66	CrB2, Cr2AlB2, Mn2AlB2
1	Cr2AlB2	1	Cr2AlB2, CrB2

Table 2. Calculated and experimental LPs and V_uc of (Mn_1-xCr_x)₂AlB₂ solid solutions.

Calculated					Experimental
x	a (Å)	b (Å)	c (Å)	V (Å^3)	x	a (Å)	b (Å)	c (Å)	V (Å^3)
0	2.895	11.054	2.828	90.50	0	2.921	11.066	2.897	93.62
					0.10	2.921	11.049	2.906	93.78
0.33	2.895	10.972	2.886	91.68	0.25	2.921	11.011	2.932	94.29
0.50	2.895	10.968	2.910	92.38	0.50	2.921	10.985	2.950	94.65
0.66	2.899	10.968	2.923	92.96	0.75	2.924	11.004	2.964	95.37
					0.90	2.932	11.033	2.970	95.97
1.00	2.9231	11.042	2.931	94.61	1.00	2.937	11.047	2.968	96.30

Table 3. Experimental and calculated LPs and V_uc for (Mn_1-xCr_x)₃AlB₄ with disorder (D) and order (O) of Mn and Cr.

Calculated					Experimental
x	a (Å)	b (Å)	c (Å)	V (Å^3)	x	a (Å)	b (Å)	c (Å)	V (Å^3)
0.00	2.834	2.935	8.145	67.76
0.33 (O)	2.830	2.942	8.131	67.69
0.33 (D)	2.881	2.934	8.107	68.53
0.66 (O)	2.934	2.950	8.034	69.53	0.66	2.949	2.985	8.054	70.90
0.66 (D)	2.918	2.933	8.073	69.10
1.00	2.937	2.937	8.081	69.70	1.00	2.945	2.968	8.072	70.57

Figure 3. a) XRD patterns of (Mn_1-xCr_x)₂AlB₂ sold solutions reacted at 1050°C for 5 h as a function of x. Si powder was added as a reference. b) Lattice parameters, and c) unit cell volumes of (Mn_1-xCr_x)₂AlB₂ solid solutions as a function x. Solid lines and symbols denote the experimental LPs; dashed lines and open symbols, denote calculated LPs.

Figure 4. Structural characteristics of (Mn_1-xCr_x)₃AlB₄ solid solutions, a) XRD patterns of Cr₃AlB₄ and (Mn_0.33Cr_0.66)₃AlB₄ powders b) Lattice parameters, and c) unit cell volume as a function of Cr substitution. Solid lines and symbols denote experimental LPs; dashed lines and open symbols, denote calculated LPs.