First-Principles study of Thermal and Elastic Properties of Al2O3

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
1. Introduction
4. Conclusions

• Alumina (a-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 a 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 a 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 a-Al2O3 at zero pressure. Lines denote
theoretical spectrum and discrete squares denote
experimental data1.
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 a-Al2O3 as a function of temperature and
volume per atom.

• Bulk crystalline a-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 a-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
coefficients2-8 of a-Al2O3 as a function of
temperature at zero pressure.
Figure 6. Comparison of calculated isobaric heat
capacity and entropy of a-Al2O3 with experimental
data9 as a function of temperature at zero
pressure.
Figure 7. Comparison of the theoretical
normalized adiabatic bulk modulus (at T0K) of
a-Al2O3 with measurements10 as a function of
temperature.

• Elasticity of a 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 C22C11
C55C44 C66(C11-C12)/2 C23C13 For
Orthorhombic symmetry C140
Figure 8, 9. Calculated elastic constants of
a-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