Kinetic MC: Ordering and Vacancy Migration in 2-D Binary Alloy
KMC is only important really if you are planning to model dynamic events,
such as radiation damage effects, diffusion constants, adhesion, surface
migration, step growth, size changes in ordering domain versus time, and so on.
In these cases, things really depend on a time scale which must be known,
as opposed to usual MC which typcial reports things in MC time steps
(whatever they are).
Getting Started
- Download the 2-D Kinetic Monte Carlo code
ordering.f,
and Save As ordering.f .
ordering.f - The source code.
Top lines of code give compiler options for most workstations.
ordera.res, orderb.res, orderv.res, and order.res -
The outputs are described in source. The code will not
overwrite the output files, so, if you want to keep them,
you must rename them.
- Download the input data
order.data,
and Save As order.data .
order.data - Example input DATA file.
NOTE: The total number of vacancy jumps and sub-blocks over
which averages are performed are indicated in order.data.
You can explore what these do but notice that increasing vacancy jumps
by order of magntiude affects the elapsed time between blocks.
If you do anything, it is better to increase jumps. You MUST do this
when nearing a phase transition, e.g., 80-100 Million, whereas much above
or below this temperature 10-20 Million may be fine. Experiment a litte.
NOTE: Do not forget that to get reasonable results one must always
average over multiple MC runs. You cannot just run one temperature for one
80 Million Steps and stop.
Question 1 - Flowchart
Look at the source ordering.f and write a flowchart
describing this KMC code and application. In addition, describe how the time is
incremented as it is and how the rates for the vacancy jumps are determined and why
for both. Also, describe what SRO and LRO is telling you.
Question 2 - Initialization with Random Configuration
Set the INIT CONF parameter to 3, which starts with a random configuration,
including the position of the vacancy. Start Finding (or bracketing) the
transition temperature for this ordering alloy by trying different Temperature.
For the alloy interactions in the DATA file, try
T=260 K, 560 K, 660 K, 860 K. How does temperature affect the KMC time?
What is the SRO and LRO help you at each temperature?
NOTE: Run for cB=0.50 A-B alloy, which is equivalent
to square lattice Ising Model, or an 2-D FCC CuAu.
The pairwise interactions interaction have been set to VAA=VAB=0
and BB= -0.05 eV, so as to produce an ordering (AFM) type phase diagram.
We know that 2D Ising Model has Tcrit= (2/ln(1 + sqrt(2))/4 (the z=4
nearest-neighbors being just normalization in this code). Therefore, Tcrit=
0.5673 eV = 658 K. Hence you know your answer here before you start!
NOTE: The nearer the Tcrit the more the jump
attempts must be increased.
Question 3 - Initialization with Ordered Configuration
Set the INIT CONF parameter to 1, which starts with a ordered configuration.
Repeat the same temperatures in reverse order as in #2.
What happens now?
Question 4 - Special Effects
At some density dependent upon temperature and interactions,
vacancies exist in thermal equilibrium in real materials.
Additional vacancies can be created in a number of ways; for example,
radiation damage will create a very large number of excess vacancies.
Typically, it is considered that radiation damage will disorder an alloy,
such as the 2-dimensional one that you are studying. Why? From what you have
found from Questions 2 and 3, consider an additional rate in the KMC arising
from radiation damage. How would you include in the KMC code?
Explain what will happen to the low-T portion of the phase boundaries,
rather than the usual phase LOOP meeting at c=0.50 exactly at T=0 K.
- We have a 2-D Kinetic Monte Carlo code with Ballistic Jumps included,
but why don't you give it a try first by modifying the MC portion of the code.
The neighbor list update is really the tricky part, if you assume the
ballistic jumps arise from a constant rate independent of environment.
D. Johnson, November 30, 1998