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MAX phases

Definition

The MAX phases are layered, hexagonal carbides and nitrides have the general formula: Mn+1AXn, (MAX) where n = 1 to 3, M is an early transition metal, A is an A-group (mostly IIIA and IVA, or groups 13 and 14) element and X is either carbon and/or nitrogen. The layered structure consists of edge-sharing, distorted XM6 octahedra interleaved by single planar layers of the A-group element.


For more information check the following link :

https://en.wikipedia.org/wiki/MAX_phases


A list of the MAX phases known to date, in both bulk and thin film form:[1]
211 Phases312 Phases413 Phases
Ti2CdC, Sc2InC, Ti2AlC, Ti2GaC, Ti2InC, Ti2TlC, V2AlC, V2GaC, Cr2GaC, Ti2AlN, Ti2GaN, Ti2InN, V2GaN, Cr2GaN, Ti2GeC, Ti2SnC, Ti2PbC, V2GeC, Cr2AlC, Cr2GeC, V2PC, V2AsC, Ti2SC, Zr2InC, Zr2TlC, Nb2AlC, Nb2GaC, Nb2InC, Mo2GaC, Zr2InN, Zr2TlN, Zr2SnC, Zr2PbC, Nb2SnC, Nb2PC, Nb2AsC, Zr2SC, Nb2SC, Hf2InC, Hf2TlC, Ta2AlC, Ta2GaC, Hf2SnC, Hf2PbC, Hf2SnN, Hf2SC, Zr2AlCTi3AlC2,
Ti3GaC2,
Ti3InC2, V3AlC2,
Ti3SiC2,
Ti3GeC2,
Ti3SnC2,
Ta3AlC2,
Zr3AlC2
Ti4AlN3,
V4AlC3,
Ti4GaC3,
Ti4SiC3,
Ti4GeC3,
Nb4AlC3,
Ta4AlC3,


Crystal structure  

The max phase compounds occured in 2 structures: hexagonal (P63/mmc)  and cubic (Fm3m).

Hexagonal structure

ExampleTi3AlC2

The space group: P63/mmc

Wyckoff Positions of Group 194 (P63/mmc)

MultiplicityWyckoff
letter
Site
symmetry
Coordinates
24l1
(x,y,z)(-y,x-y,z)(-x+y,-x,z)(-x,-y,z+1/2)
(y,-x+y,z+1/2)(x-y,x,z+1/2)(y,x,-z)(x-y,-y,-z)
(-x,-x+y,-z)(-y,-x,-z+1/2)(-x+y,y,-z+1/2)(x,x-y,-z+1/2)
(-x,-y,-z)(y,-x+y,-z)(x-y,x,-z)(x,y,-z+1/2)
(-y,x-y,-z+1/2)(-x+y,-x,-z+1/2)(-y,-x,z)(-x+y,y,z)
(x,x-y,z)(y,x,z+1/2)(x-y,-y,z+1/2)(-x,-x+y,z+1/2)
12k.m.
(x,2x,z)(-2x,-x,z)(x,-x,z)(-x,-2x,z+1/2)
(2x,x,z+1/2)(-x,x,z+1/2)(2x,x,-z)(-x,-2x,-z)
(-x,x,-z)(-2x,-x,-z+1/2)(x,2x,-z+1/2)(x,-x,-z+1/2)
12jm..
(x,y,1/4)(-y,x-y,1/4)(-x+y,-x,1/4)(-x,-y,3/4)
(y,-x+y,3/4)(x-y,x,3/4)(y,x,3/4)(x-y,-y,3/4)
(-x,-x+y,3/4)(-y,-x,1/4)(-x+y,y,1/4)(x,x-y,1/4)
12i.2.
(x,0,0)(0,x,0)(-x,-x,0)(-x,0,1/2)
(0,-x,1/2)(x,x,1/2)(-x,0,0)(0,-x,0)
(x,x,0)(x,0,1/2)(0,x,1/2)(-x,-x,1/2)
6hmm2
(x,2x,1/4)(-2x,-x,1/4)(x,-x,1/4)(-x,-2x,3/4)
(2x,x,3/4)(-x,x,3/4)
6g.2/m.
(1/2,0,0)(0,1/2,0)(1/2,1/2,0)(1/2,0,1/2)
(0,1/2,1/2)(1/2,1/2,1/2)
4f3m.
(1/3,2/3,z)(2/3,1/3,z+1/2)(2/3,1/3,-z)(1/3,2/3,-z+1/2)
4e3m.
(0,0,z)(0,0,z+1/2)(0,0,-z)(0,0,-z+1/2)
2d-6m2
(1/3,2/3,3/4)(2/3,1/3,1/4)
2c-6m2
(1/3,2/3,1/4)(2/3,1/3,3/4)
2b-6m2
(0,0,1/4)(0,0,3/4)
2a-3m.
(0,0,0)(0,0,1/2)


The MAX solid solutions (Zr3-xTix)AlC2 crystallize in the hexagonal structure in the space group P63/ mmc (No. 194) [49, 50]. The transition metal atoms M(1) and M(2) occupy the Wyckoff positions 2a and 4f (zM * 0.12), respectively. The Al atoms reside in 2b atomic sites. The C atoms take up the 4f (zM * 0.07) atomic positions with different z-values. The unit cell of 312 MAX phases consists of two formula units (Check the Fig. ).


Reference: https://core.ac.uk/download/pdf/81919665.pdf




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