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--- exercises:2017_ethz_mmm:mc_and_kmc_2 [2017/03/08 16:03] – created dpasserone
+++ exercises:2017_ethz_mmm:mc_and_kmc_2 [2020/08/21 10:15] (current) – external edit 127.0.0.1
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-The hexaiodobenzene molecule shown in the image, when deposited on a noble metal substrate such as
+====== Kinetic Monte Carlo simulations for the diffusion of molecules on  a substrate ======
+=====
+The  molecule shown in the image (hexaiodo-substituted
+macrocycle cyclohexa-m-phenylene (CHP) ), when deposited on a noble metal substrate such as
 Cu(111) , Ag(111) or Au(111), at room temperature looses the I atoms and starts diffusing.
+{{:exercises:2017_ethz_mmm:hexaiodobenzene.jpg?400|}}
 The relative probability of diffusion and of binding to a neighboring molecule
 determine the shape of the network that will be obtained.
-The experiments performed at Empa [ [[http://dx/doi.org/10.1021/ja107947z]] J. AM. CHEM. SOC. 2010, 132, 16669–16676 ] shows that on a Cu substrate dendrites will form
+The experiments performed at Empa [ [[http://dx.doi.org/10.1021/ja107947z]] J. AM. CHEM. SOC. 2010, 132, 16669–16676 ] shows that on a Cu substrate dendrites will form
 while on a Au substrate 2D networks will form.
+{{:exercises:2017_ethz_mmm:dendrites.jpg?400|}}
+<note tip>
 The python program KMC.py will allow you to simulate the diffusion and binding of molecules
-once the energy barriers for the diffusion event and for the binding event as well as the simulatin temperature will be defined.
+once the energy barriers for the diffusion event and for the binding event as well as the simulation temperature will be defined.
-During the execution the program shows snapshots of the positins of the molecules.
+During the execution the program shows snapshots of the positions of the molecules.
+{{:exercises:2017_ethz_mmm:final_0.1_300_0.1_0.1.png?400|}}
 Molecules free to diffuse will be represented via blue dots.
-Molecules that irreversibely formed a bond with a neighboring molecule will be represented by red dots.
+Molecules that irreversibly formed a bond with a neighboring molecule will be represented by red dots.
+At the end of the execution a snapshot of the final configuration of the system is saved an image file.
+The program asks you for some input:
+<code>
+coverage
+update graph each steps
+temperature in K
+diffusion barrier
+binding barrier
+</code>
+</note>
+<note warning>
+**TASK 1**
+execute the program with the following parameters:
+<code>
+coverage 0.1
+update graph each steps 500
+number of steps 100000
+temperature in K 300
+diffusion barrier 0.1
+binding barrier 0.1
+</code>
+Observe how events occur.
+Observe how time evolves.
+Did the job perform all the 100000 steps? Why?
+Observe the patterns obtained.
+</note>
+<note warning>
+**TASK 2**
+execute the program with the following parameters:
+<code>
+coverage 0.1
+update graph each steps 500
+number of steps 100000
+temperature in K 300
+diffusion barrier 0.3
+binding barrier 0.4
+</code>
+Do you notice differences in the way events occur?
+How is evolving time compared to the previous case?
+How does the final geometry differ form the previous case?
+</note>
+<note tip>
+Now have a look at the python code.
+The MAIN section
+<code>
+#### MAIN KMC LOOP
+t=0
+#### at the beginning we have to check possible events for all molecules
+tobeupdated=[iu for iu in range(len(molecules))]
+possible_events=[]
+for i in range(nsteps):
+    #### check possible events for selected set of molecules
+    possible_events=possible_events+events(molecules,tobeupdated,nx,ny)
+    if possible_events==[]:
+       print "no more events possible"
+       break
+    #### compute total rate (can be imporved)
+    R=total_rate(possible_events,rates)
+    #### decide which event to apply
+    selected_event=find_event(R,rates,possible_events)
+    #### apply the event end update partially the list of events
+    possible_events,tobeupdated=apply_event(molecules,selected_event,possible_events)
+    #### update time
+    rho2=np.random.random()
+    dt=-np.log(rho2)/R
+    t=t+dt
+</code>
+is very simple and reflects the basic steps of the KMC approach.
+On the contrary, the function needed to create the list of events is quite complex:
+<code>
+def events(m,selection,nx,ny):
+    allevents=[]
+    set=[]
+    #### list of first neighbors (relative position)
+    set.append([[0,0,1,0],[1,0,0,0],[0,1,1,0],[-1,1,1,0],[-1,0,0,0],[-1,0,1,0]])
+    set.append([[1,-1,-1,0],[1,0,0,0],[1,0,-1,0],[0,0,-1,0],[-1,0,0,0],[0,-1,-1,0]])
+    for i in selection:
+        le=[]
+        #### consider only molecules that are not binded
+.
+.
+.
+</code>
+</note>
+<note warning>
+**TASK 3**
+Have a look on the section of the code that create the list of events,
+comment on which are the critical points in setting up a KMC simulation
+to describe a real process.
+**TASK 4**
+At each step of the simulaiton the list of possible events is created (or, betetr, updated)
+an event is chosen randomly and is then actuated.
+Would it be possible to execute simultaneously more events at each KMC step?
+</note>