First-Principles study of Thermal and Elastic Properties of Al 2 O 3

1. First-Principles study of Thermal and Elastic Properties of Al2O3 Bin Xu and Jianjun Dong, Physics Department, Auburn University, Auburn, AL 36849 3. Results 4. Conclusions 1. Introduction • Alumina (α-Al2O3) nanoparticles • Phonon dispersion • Phonon spectrum is computationally challenging. • We have developed new codes to optimize the calculation. It is proved that the codes are efficient and general for super cell model as large as 160 atoms of any crystal structure. • Our calculation is in agreement with experimental data. • Thermal properties • Our theoretical thermal expansion coefficient, heat capacity, entropy and bulk modulus agree well with measured results. • The agreement ensures the validity of our calculation. • Elasticity of α and Rh2O3(II) phase • The high strength of Al2O3 is associated with the large elastic constants. • The newly theoretically predicted Rh2O3(II) phase is only 2% larger in density than α phase and this is in consistency with the similarity of calculated elastic constants of these two phases. Application of ceramic nano particle in polymer based composite materials: Small ceramic particles are known to enhance the mechanical and tribological properties. Figure 3. LDA calculation of (a) phonon dispersion relations, (b) vibrational density of states of α-Al2O3 at zero pressure. Lines denote theoretical spectrum and discrete squares denote experimental data[1]. Primary particles have a size of 13 nm. They stick together and form agglomerates in the size of some microns. Figure 4. Calculated Helmholtz free energies per atom of α-Al2O3 as a function of temperature and volume per atom. • Bulk crystalline α-Al2O3 • Excellent material properties and extensive technology applications: • Large elasticity • High strength and hardness • Chemically inert • Coating as thin-film on devices • Wear applications and cutting tools • Thermal properties References [1] H. Shober, et al, Z. Phys. B: Condens. Matter 92, 273 (1993) [2] J. Hama, et al, Phys. Chem. Minerals 28, 258 (2001) [3] Wachtman Jr JB, et al, J. Am. Ceram. Soc. 45, 319 (1962) [4] Schauer A, Can. J. Phys. 43, 523 (1965) [5] Amatuni AN, et al, High Temp-High Pressure 8, 565 (1976) [6] Aldebert P, et al, High Temp-High Pressure 16, 127 (1984) [7] Fiquet G, et al, Phys. Chem. Miner. 27, 103 (1999) [8] White GK, et al, High Temp-High Pressure 15, 321 (1983) [9] Furukawa GT, et al, J. Res. Natl. Bur. Stand. 57, 67 (1956) [10] Goto T, et al, J Geophys. Res. 94, 7588 (1989) Figure 1. Crystal structure of alumina: (a) The side view of a ball-and-stick model of α-Al2O3, with the vertical direction along the hexagonal-close-pack axis. (b) Al atoms are 100% octahedrally bonded. (c) And O atoms are 100% tetrahedrally bonded. Figure 5. Comparison of the present theoretical calculation with measured bulk thermal expansion coefficients[2-8] of α-Al2O3 as a function of temperature at zero pressure. Figure 6. Comparison of calculated isobaric heat capacity and entropy of α-Al2O3 with experimental data[9] as a function of temperature at zero pressure. Figure 7. Comparison of the theoretical normalized adiabatic bulk modulus (at T=0K) of α-Al2O3 with measurements[10] as a function of temperature. • Elasticity of α and Rh2O3(II)-Al2O3 2. Computational Methodologies • Structure Optimization and Total Energy Calculation • First-Principles Quantum Mechanics Theory: Plane wave, Pseudo-potential, Density Functional Theory (PW-PP-DFT) • Thermodynamic Potentials at finite temperatures • Statistical Quasi-Harmonic Approximation (QHA) Acknowledgements This work is supported by National Science Foundation (Grant No. EPS-0447675 and HRD-0317741). Blue color denote Cij that is not independent. For rhombohedral symmetry: C22=C11; C55=C44; C66=(C11-C12)/2; C23=C13 For Orthorhombic symmetry: C14=0 Figure 8, 9. Calculated elastic constants of α-Al2O3 and Rh2O3(II)-Al2O3 as a function of hydrostatic pressure. Symbols denote the calculated data at a certain pressure and lines are from linear fitting. F Table 1. Linear pressure dependence of Cij from the fit to calculated elastic constants. 2007 Alabama EPSCoR Annual Meeting, University of Alabama in Huntsville, February 13, 2007