first-principles study of thermal and elastic properties of al 2 o 3 bin xu and jianjun dong,...

First-Principles study of Thermal and Elastic Properties of Al2O3 Bin Xu and Jianjun Dong, Physics Department, Auburn University, Auburn, AL 36849

1. Introduction

2. Computational Methodologies

3. Results 4. Conclusions

References

Acknowledgements

2007 Alabama EPSCoR Annual Meeting, University of Alabama in Huntsville, February 13, 2007

0

1( , ) ( ) ( ) ln(1 )

2Bk T

static BF T V E V d g k T e

0

200

400

600

800

1000

Fre

qu

en

cy:

(cm

-1)

A Z D

(a) Phonon dispersion (b) Density of State

arb. units

-Al2O

3

Pressure: 0GPa300

600900

1200

1500

1800

-8.7

-8.6

-8.5

-8.4

-8.3

-8.2

-8.1

-8.0

-7.9

7.07.5

8.08.5

9.09.5

10.010.5

0 500 1000 1500 20000.0

5.0x10-6

1.0x10-5

1.5x10-5

2.0x10-5

2.5x10-5

3.0x10-5

3.5x10-5

4.0x10-5

-Al2O

3

The

rmal

exp

ansi

on c

oeffi

cien

t: (

K-1)

Temperature: T(K)

TheoryExpt.

Wachtman et al. (1962) Schauer (1965) Amatuni et al. (1976) Aldebert & Traverse (1984) Fiquet et al. (1999) White and Roberts (1983)

P=0GPa

0 500 1000 1500 2000

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

BS(0)=242.47GPa

BS(0)=253.85GPa

BS(0)=256.85GPa

BS(0)=251.97GPa-Al

2O

3

Temperature: T(K)

Nor

mal

ized

adi

abat

ic B

ulk

Mod

ulus

: BS/B

S(T

=0K

)

TheoryExpt.

Goto et al. (1989) Chung & Simmons (1968) Teffet (1966)

P=0GPa

21 1

P

V G

V T V T P

V

FS

T

PP

SC T

T

P P

S TTV V

C C PB B V

C C V

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.

Bulk crystalline α-Al2O3

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-Al2O3 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-Al2O3 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-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.

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.

Excellent material Excellent material properties and extensive properties and extensive technology applications:technology applications:•Large elasticity•High strength and hardness•Chemically inert•Coating as thin-film on devices•Wear applications and cutting tools

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

Table 1. Linear pressure dependence of Cij 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)

0 500 1000 1500 20000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0

1

2

3

4

5

6

7-Al2O

3

Iso

ba

ric

he

at c

ap

aci

ty: C

P(k

B/a

tom

)

Temperature: T(K)

En

tro

py:

S(k

B/a

tom

)

Theory C

P

SExpt.

Furukawa et al. (1956) Furukawa et al. (1956)

P=0GPa1k

B/atom=41.57J/mol/K

Phonon dispersion Phonon spectrum is computationally challenging. We have developed new codes to optimize the calculation. It is pr

oved 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.

This work is supported by National Science Foundation (Grant No. EPS-0447675 and HRD-0317741).

Elasticity of α and Rh2O3(II)-Al2O3

Thermal properties

Alumina (α-Al2O3) 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 particlApplication of ceramic nano particle in polymer based composite mate in polymer based composite materials:erials:Small ceramic particles are known to enhance the mechanical and tribological properties.

F

0 10 20 30 40 500

100

200

300

400

500

600

700

Pressure: P(GPa)

Ela

stic

Con

stan

ts: C

ij (

GP

a)

C11

C12 C13 C14 C33 C44

-Al2O

3

0 20 40 60 80 100 120 1400

100200300400500600700800900

100011001200

C11

C22

C33

C44

C55

C66

C12

C13

C23

Ela

stic

Con

stan

ts: C

ij (G

Pa)

Pressure: P(GPa)

Rh2O

3(II)-Al

2O

3