First-Principles study of Thermal and Elastic Properties of Al 2 O 3 Bin Xu and Jianjun Dong, Physics Department, Auburn University, Auburn, AL Introduction 2. Computational Methodologies 3. Results 4. Conclusions References Acknowledgements 2007 Alabama EPSCoR Annual Meeting, University of Alabama in Huntsville, February 13, 2007 Figure 1. Crystal structure of alumina: (a) The side view of a ball-and-stick model of α-Al 2 O 3, 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. Bulk crystalline α-Al 2 O 3 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) Figure 4. Calculated Helmholtz free energies per atom of α-Al 2 O 3 as a function of temperature and volume per atom. Figure 3. LDA calculation of (a) phonon dispersion relations, (b) vibrational density of states of α-Al 2 O 3 at zero pressure. Lines denote theoretical spectrum and discrete squares denote experimental data [1]. Figure 5. Comparison of the present theoretical calculation with measured bulk thermal expansion coefficients [2- 8] of α-Al 2 O 3 as a function of temperature at zero pressure. Figure 6. Comparison of calculated isobaric heat capacity and entropy of α-Al 2 O 3 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- Al 2 O 3 with measurements [10] as a function of temperature. Figure 8, 9. Calculated elastic constants of α-Al 2 O 3 and Rh 2 O 3 (II)-Al 2 O 3 as a function of hydrostatic pressure. Symbols denote the calculated data at a certain pressure and lines are from linear fitting. 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 Blue color denote C ij that is not independent. For rhombohedral symmetry: C 22 =C 11 ; C 55 =C 44 ; C 66 =(C 11 -C 12 )/2; C 23 =C 13 For Orthorhombic symmetry: C 14 =0 Table 1. Linear pressure dependence of C ij from the fit to calculated elastic constants. [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) 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 Rh 2 O 3 (II) phase The high strength of Al 2 O 3 is associated with the large elastic constants. The newly theoretically predicted Rh 2 O 3 (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. This work is supported by National Science Foundation (Grant No. EPS and HRD ). Elasticity of α and Rh 2 O 3 (II)-Al 2 O 3 Thermal properties Alumina (α-Al 2 O 3 ) nanoparticles Primary particles have a size of 13 nm. They stick together and form agglomerates in the size of some microns. Application of ceramic nano particle in polymer based composite materials: Small ceramic particles are known to enhance the mechanical and tribological properties. F