1. Ab Initio calculations of MAX phases M 2 TlC (M =Ti, Zr, Hf), M 2 GaN, (M = Ti, V, Cr ) S. V. Khare 1, J. A. Warner 2,3, and S. K. R. Patil 3 1.Department of Physics and Astonomy University of Toledo Ohio 43606 2. Department of Mechanical and Industrial Engineering University of Toledo Ohio 43606 3. Department of Physics, University of Wisconsin at Madison Ohio 43606 http://www.physics.utoledo.edu/~khare/

2. 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 Z M is the internal degree of freedom within the unit cell *M.W. Barsoum, Prog. Sol. Stat. Chem. 28 (2000) 201. HEXAGONAL MAX 211 PHASE M n+1 AX n (n=1,2,3) ZMZM

3. Atoms in unit cell P Q R P Q R are three sites in hcp packing. P X R M Q A R M P X Q M R A Q M

4. M 2 AX, M = transition metal (cyan), A = A group element, X = C or N.

5. Motivation for M 2 TlC based compounds M = Ti, Zr, Hf From Sun et al., PRB 70, 92102 (2004).

6. Lattice constants and B for M 2 TlC, M = Ti, Hf, Zr B values lowest of all MAX phases studied so far. All results in this talk are with DFT-GGA, VASP.

7. DOS Results for M 2 TlC, M = Ti, Zr, Hf DOS at E f decreases from Ti- Zr-Hf.

8. LDOS Results for M 2 TlC, 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.

9. Motivation for M 2 GaN based compounds M = Ti, V, Cr

10. Lattice constants and B for M 2 GaN, M = Ti, V, Cr

11. DOS Results for M 2 GaN, M = Ti, V, Cr DOS at E f increases from Ti-V- Cr.

12. LDOS Results for M 2 GaN, 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 both hybridization peaks go away from their respective Ef values. Similar trend for Ti 2 AlC, Cr 2 AlC, Cr 2 GeC, in data from Sun et al., PRB 70, 92102 (2004). B values seem to correlate with this trend.

13. Conclusions of work on MAX phases 1.Calculated lattice constants and bulk moduli of Ti 2 GaN, V 2 GaN, and Cr 2 GaN. 2.Calculated lattice constants and bulk moduli of Ti 2 TlC, Zr 2 TlC, and Hf 2 TlC. 3.Calculated LDOS and DOS of Ti 2 GaN, V 2 GaN, and Cr 2 GaN. 4.Calculated LDOS and DOS of Ti 2 TlC, Zr 2 TlC, and Hf 2 TlC. 5.All six MAX phases are conducting. The M-A bonds are weaker than the M-X bonds. 6. Ti 2 TlC, Zr 2 TlC, and Hf 2 TlC 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).

14. 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

15. Thank you!

16. 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

17. Barsoum’s Table *M.W. Barsoum, Prog. Sol. Stat. Chem. 28 (2000) 201.

18. Outline About MAX phases MAX phases - calculations Conclusions