Table 1 The thermoelastic diffusion parameters of Al₂O₃

Reference temperature

T ₀

293

K

Density

ρ ^′

3900

kg ⋅ m^‐3

Specific heat

C _ε

900

J ⋅ kg⁻¹ ⋅ K⁻¹

Thermal conductivity

k ^′

27

W ⋅ m⁻¹ ⋅ K⁻¹

Thermal expansion coefficient

α _t

8.0 × 10⁻⁶

K⁻¹

Elastic modulus

E

380

GPa

Poisson ratio

ν

0.22

Thermal relaxation time

τ ₀

0.2

s

Diffusion expansion coefficient

α _c

2.34 × 10⁻⁴

m³ ⋅ kg

Diffusion coefficient

D

0.63 × 10⁻⁸

kg ⋅ s ⋅ m⁻³

Measures of the thermodiffusion effects

a ^′

2.32 × 10⁴

m² ⋅ s⁻² ⋅ K⁻¹

Measures of the diffusive effects

b ^′

3.061 × 10⁶

m⁵ ⋅ kg⁻¹ ⋅ s⁻²

Diffusion relaxation time

τ

0.02

s

Volume of vacancy

Ω

2.7 × 10⁻²⁹

m³

Boltzman constant

k

1.3806505 × 10⁻²³

Enthalpy of vacancy motion

H _m

3.8

eV