Ab Initio calculations of MAX phases M2TlC (M =Ti, Zr, Hf), M2GaN, (M = Ti, V,

Cr )S. V. Khare1, J. A. Warner2,3, and S. K. R. Patil3

1. Department of Physics and AstonomyUniversity of Toledo

Ohio 436062. Department of Mechanical and Industrial Engineering

University of ToledoOhio 43606

3. Department of Physics, University of Wisconsin at Madison

Ohio 43606

http://www.physics.utoledo.edu/~khare/

What are MAX Phases?

• M = transition metal = • A = A-group element =• X = C or N =• Electrically and thermally

conductive materials• Relatively soft• Resistant to Thermal

Shock• Damage Tolerant• ZM is the internal degree

of freedom within the unit cell

*M.W. Barsoum, Prog. Sol. Stat. Chem. 28 (2000) 201.HEXAGONAL MAX 211 PHASE

Mn+1AXn (n=1,2,3)

ZM

Atoms in unit cell

PQ

RP Q R are three sites in hcp packing.

PXRMQARMPXQMRAQM

M2AX, M = transition metal (cyan), A = A group element, X = C or N.

Motivation for M2TlC based compounds M = Ti, Zr, Hf

From Sun et al., PRB 70, 92102 (2004).

Lattice constants and B for M2TlC, M = Ti, Hf, Zr

B values lowest of all MAX phases studied so far.

All results in this talk are with DFT-GGA, VASP.

DOS Results for M2TlC,

M = Ti, Zr, Hf

DOS at Ef decreases from Ti-Zr-Hf.

LDOS Results for M2TlC,

M = Ti, Zr, Hf

1. C-p electrons in M-d C-p hybridization increase from

Ti-Zr-Hf.

2. M-d C-p bonding is stronger than M-d Tl-p bonding.

Motivation for M2GaN based compounds M = Ti, V, Cr

Lattice constants and B for M2GaN, M = Ti, V, Cr

DOS Results for M2GaN,

M = Ti, V, Cr

DOS at Ef increases from Ti-V-Cr.

LDOS Results for M2GaN, M = Ti, V, Cr

B = 158 GPa

B= 170 Gpa

B = 180 GPa

M-d to N-p bonding is stronger than M-d to Ga-p bonding.

As we go from Ti-V-Cr bothhybridization peaks go away from their respective Ef values. Similar trend for Ti2AlC, Cr2AlC, Cr2GeC, in data from Sun et al., PRB 70, 92102 (2004).

B values seem to correlate with this trend.

Conclusions of work on MAX phases1. Calculated lattice constants and bulk moduli of Ti2GaN, V2GaN, and Cr2GaN.

2. Calculated lattice constants and bulk moduli of Ti2TlC, Zr2TlC, and Hf2TlC.

3. Calculated LDOS and DOS of Ti2GaN, V2GaN, and Cr2GaN.

4. Calculated LDOS and DOS of Ti2TlC, Zr2TlC, and Hf2TlC.

5. All six MAX phases are conducting. The M-A bonds are weaker than the M-X bonds.

6. Ti2TlC, Zr2TlC, and Hf2TlC have the lowest bulk moduli of all MAX phases studied to date.

J. A. Warner, S. K. R. Patil, S. V. Khare, R. S. Masiuliniec, APL 88, 101911 (2006).

Institutional Support

University of Toledo URAF Summer Fellowship

University of Toledo, Board of Trustees

University of Toledo parallel computing cluster

Ohio Supercomputer cluster

NSF REU program at University of Toledo

Thank you!

Ab initio method details

• LDA, Ceperley-Alder exchange-correlation functional as parameterized by Perdew and Zunger

• Used the VASP code with generalized ultra-soft Vanderbilt pseudo-potentials and plane wave basis set

• Bulk supercell approach with periodic boundary conditions in all three dimensions

• Energy cut-offs of 300 eV for MAX phases, dense k-point

meshes

• Forces converged till < 0.03 eV/ Å

• Used AMD Athlon dual processors at UT and OSC

Bar

soum

’s T

able

*M.W. Barsoum, Prog. Sol. Stat. Chem. 28 (2000) 201.

Outline

• About MAX phases• MAX phases - calculations• Conclusions