Table 1 Numeric value of probabilities adopted for CA model.

From: Examining oxidation in β-NiAl and β-NiAl+Hf alloys by stochastic cellular automata simulations

Diffusion at 1050 °C

Diffusive element

Diffusion though

Probability

Diffusivity (m2.s−1)

Reference

Oxygen

Ni

0

  

Oxygen

Al

0

  

Oxygen

NiO

1/ 13.3819519

4.15E-14

50

Oxygen

Al2O3

1/25.6716204

2.13E-26

51

Oxygen

Hf

O

  

Oxygen

HfO2

1/1000

 

*

Al

Al2O3

1/1000

 

**

Random movement of atoms

Element

Direction of movement

Exchanging position with

Probability

 

Al

Up

Ni

0.005

 

Ni

Down

Al

0.0005

 

Hf

Up

Al

0.005

 

Al

Down

Hf

0.0025

 

O

Random

N

1

 

Decomposition

Primary cell

Neighbor

Result

Probability

 

Al

NiO

Primary = Al2O3

1/10,000***

 
  

Neighbor = Ni

  
  1. *Chosen randomly to account for the large size of HfO2 creating diffusion barrier.
  2. **Chosen randomly to signify the very slow diffusion of Al through Al2O3.
  3. ***Chosen randomly, but to signify the slowest process of all processes considered.
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