Interfaces¶
This tutorial will show how to obtain the results presented in this paper: Therrien, Félix, Peter Graf, and Vladan Stevanović. “Matching crystal structures atom-to-atom.” The Journal of Chemical Physics 152.7 (2020): 074106.
This assumes that you have installed p2ptrans (see Installation).
Top and Bottom Structures¶
In this tutorial, we will find the orientation between Diamond Si (110) and 6H-SiC (001).
First let’s create a directory and move our working directory to it:
mkdir tutorial2
cd tutorial2
The initial and final structure must be given in the POSCAR format.
Let’s create the input file for Si and let’s name it POSCAR_Si:
Si
5.43
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
Si
8
Direct
-0.125 -0.125 -0.125
-0.125 0.375 0.375
0.375 -0.125 0.375
0.375 0.375 -0.125
0.125 0.125 0.125
0.125 0.625 0.625
0.625 0.125 0.625
0.625 0.625 0.125
Similarly for SiC, let’s create the file POSCAR_SiC:
SiC
1.000000
1.54064500000000 -2.66847541642695 0.00000000000000
1.54064500000000 2.66847541642695 0.00000000000000
0.00000000000000 0.00000000000000 15.11975999999338
C Si
6 6
Direct
0.00000000000000 0.00000000000000 0.12540000000000
0.00000000000000 0.00000000000000 0.62540000000000
0.33333333333333 0.66666666666667 0.29215000000000
0.66666666666667 0.33333333333333 0.79215000000000
0.33333333333333 0.66666666666667 -0.04150000000000
0.66666666666667 0.33333333333333 0.45850000000000
0.00000000000000 0.00000000000000 0.00000000000000
0.00000000000000 0.00000000000000 0.50000000000000
0.33333333333333 0.66666666666667 0.16675000000000
0.66666666666667 0.33333333333333 0.66675000000000
0.33333333333333 0.66666666666667 0.83350000000000
0.66666666666667 0.33333333333333 1.33350000000000
Running the algorithm¶
Now that we have the bottom (substrate) and top structures, we need to specify the miller indices of the interfacial plane in both structures along with the bonding rule. Let’s run the following command:
p2pint -T POSCAR_Si [1,1,0] 1 Si -B POSCAR_SiC [0,0,1] 1 Si
Here we defined Si as the top structure (-T) and its corresponding h,k,l as (110). We defined SiC as the bottom structure (substrate) (-B) with the (001) interfacial plane. The rest of the command determines the bonding rule we set it as: 1 Si for both the top and the bottom which means “Si is part of the 1st type of bond”. This will associate, and therefore, bond the Si atoms in both structures. To bond carbon with silicon instead, the command would have been:
p2pint -T POSCAR_Si [1,1,0] 1 Si -B POSCAR_SiC [0,0,1] 1 C
Note
If a termination had two different types of atoms (which is not the case here) then the rules could be: -B POSCAR_AB [h,k,l] 1 A 2 B and -T POSCAR_CD [h,k,l] 1 C 2 D which would bond A with C and B with D at the interface between AB and CD. Similarly, one could bond A and B to C with -B POSCAR_AB [h,k,l] 1 A B and -T POSCAR_CD [h,k,l] 1 C. If you want a specific type of atom to bond to two or more other atoms you can specify it by indicating the number of bond it can form before the type of element, e.g. -B POSCAR_AB [h,k,l] 1 3A means that the atom A can form up to 3 bonds.
If you would like to store the output files in a subdirectory (e.g. outputdir) just add -o outputdir:
p2pint -T POSCAR_Si [1,1,0] 1 Si -B POSCAR_SiC [0,0,1] 1 Si -o outputdir
This should take about 10 min to run on a laptop. p2pint will automatically use all threads on your computer so the computation time will depend on the number of cores on your computer.
Note
If you do not want p2pint to use all the available threads on the computer, limit the number of threads woth:
OMP_NUM_THREADS=1 p2pint -T POSCAR_Si [1,1,0] 1 Si -B POSCAR_SiC [0,0,1] 1 Si
Analyzing the output¶
Let’s analyze the standard output of p2pint:
Total number of atoms in each disk: 200
This is the number of atoms that will be mapped together, i.e it is the size of the cost matrix, this number has a very strong influence on the computational cost of running p2pint.
Check progress in ./POSCAR_SiC-POSCAR_Si/term_000-000/progress.txt
progress.txt contains a list of the random initializations minimizations that have been started and completed.
Looking for periodic cell for peak 0...
Found cell!
Contrary to p2ptrans, p2pint can look for the best results instead of only looking the absolute minimal distance. Each potential result represents a peak in the distance vs. angle plot. By default, however, this functionality is turned off and p2pint will only give one peak, corresponding to the optimal result. Found cell! indicates that p2pint has found the cell of correspondence (Interface Cell) between the two structures.
-------OPTIMIZATION RESULTS FOR PEAK 0--------
Number of classes: 8
Number of mapped atoms: 50
Total distance between structures: -0.09168486691094771 ( -47.121009043696 )
Optimal angle between structures: 242.6019448122653
Volume stretching factor (det(T)): 0.9860348231038032
Cell volume ratio (initial cell volume)/(final cell volume): 0.7887531650921741
This block summarizes the result of the optimization. The number of classes is the number of types of connections i.e. the number of different “bonds” that were found. The total distance between the structures is the measure of how compatible they are with this choice of potential (lennard-Jones by default). The volume stretching factor indicates how much strain there is in the first layer of the top structure. The cell volume ratio indicates the ratio of specific areas of the two interfacial planes. Note that since this is a semi-coherent interface the specific area of the two planes is very different, i.e the lattices do not match in the conventional sense of lattice matching.
Note
You may not necessarily obtain the exact same result to numerical precision since p2pint uses a random exploration method to find the global minimum. Additionally, the structures have a 6-fold rotational symmetry, which mean every angle that is different by a multiple of 60 is also optimal.
-----------PERIODIC CELL-----------
Number of bonds in Interface Cell (IC): 8
Number of SiC (0 0 1) 1 cells in IC: 9.998746698318255
Number of Si (1 1 0) 0 cells in IC: 3.999999999999999
This block gives details about the Interface Cell. The number of SiC cells is not integer because of the level of precision of the classification algorithm (1e-3 by default).
Creating POSCARS for peak 0, bottom term. 0, top term 0
Creating POSCARS for peak 0, bottom term. 1, top term 0
Creating POSCARS for peak 0, bottom term. 2, top term 0
Creating POSCARS for peak 0, bottom term. 3, top term 0
Creating POSCARS for peak 0, bottom term. 4, top term 0
Creating POSCARS for peak 0, bottom term. 5, top term 0
Once the interface cell is found, p2pint will create interface structures for each combination of possible terminations. In this case Si (110) has 1 possible termination with 4 variants that are all equivalent under translation, and SiC (001) also has 1 termination with 6 variants (i.e. the terminating plane is the same, but the rest of the structure is different).
For each termination three POSCARs are created: (1,2) Representation of Si and SiC with a common cell in the plane specified at the beginning, (3) the interface between Si and SiC. For example, if you have a POSCAR viewing software like VESTA you can run:
VESTA POSCAR_SiC-POSCAR_Si/term_000-000/peak_000/var_000-000/POSCAR_interface
You can adjust the number of layers of materials on each side of the interface with the -l option and you can adjust the amount of vacuum with the -v option.
At this point your output directory should have the following structure:
outputdir
├── out.txt
├── param.dat
└── POSCAR_SiC-POSCAR_Si
└── term_000-000
├── best2d.dat
├── intoptimization.dat
├── peak_000
│ ├── var_000-000
│ │ ├── POSCAR_Bottom
│ │ ├── POSCAR_bottom
│ │ ├── POSCAR_interface
│ │ ├── POSCAR_Top
│ │ └── POSCAR_top
│ ├── var_001-000
│ │ ├── POSCAR_Bottom
│ │ ├── POSCAR_bottom
│ │ ├── POSCAR_interface
│ │ ├── POSCAR_Top
│ │ └── POSCAR_top
│ ├── var_002-000
│ │ ├── POSCAR_Bottom
│ │ ├── POSCAR_bottom
│ │ ├── POSCAR_interface
│ │ ├── POSCAR_Top
│ │ └── POSCAR_top
│ ├── var_003-000
│ │ ├── POSCAR_Bottom
│ │ ├── POSCAR_bottom
│ │ ├── POSCAR_interface
│ │ ├── POSCAR_Top
│ │ └── POSCAR_top
│ ├── var_004-000
│ │ ├── POSCAR_Bottom
│ │ ├── POSCAR_bottom
│ │ ├── POSCAR_interface
│ │ ├── POSCAR_Top
│ │ └── POSCAR_top
│ └── var_005-000
│ ├── POSCAR_Bottom
│ ├── POSCAR_bottom
│ ├── POSCAR_interface
│ ├── POSCAR_Top
│ └── POSCAR_top
└── progress.txt
Visualizing the result¶
When running p2pint, the result is saved in different files in the output directory. p2ptrans can be rerun without having to reoptimize the result. To run p2ptrans in interactive mode (-i) and use the previous result (-u) simply run:
p2pint -i -u .
The period indicates that the output is in the current directory (.), if you specified a different directory with the -o option you must provide the path to that directory. To save the images instead of displaying them:
p2ptrans -d -u .
Those two options can be used simultaneously and they can be used without the -u option.
Running the algorithm on larger systems¶
Let’s now increase the size of the disks (number of atoms used during the minimization) in order to obtain the result presented in the paper.
Tip
I like to make sure all the parameters are ok before I truly run the code. For that you can use the --test option.
p2pint -T POSCAR_Si [1,1,0] 1 Si -B POSCAR_SiC [0,0,1] 1 Si -o outputdir2 --test
That will tell you how many atoms will be in each disk which will give you an idea of how big the calculations will be–this is not always trivial when inputting two non-primitive structures of different sizes. It will also create the output directory and save the parameters of the run.
We are now ready to run the calculation:
p2pint -T POSCAR_Si [1,1,0] 1 Si -B POSCAR_SiC [0,0,1] 1 Si -n 130
Note
If you do not want to re-enter the same parameters you can also do:
p2pint -u newoutdir -m
The -m option used in concert with the -u option will use (-u) the parameters found in newoutdir and run the distance minimization (-m) on them. This will yield exactly the same results as the previous command.
The calculation should less than hour on a modern computer (9 min on 4-core Intel Core i7). If you are on a cluster, you can simply put the previous line in a submission script. p2ptrans is parallelized with OpenMP; it will automatically use all the cores in one node but cannot use multiple nodes.
Tip
I like to monitor the progress of the calculation using
grep "Opt dist" progress.txt | wc -l
This will tell you how many initial random steps have completed, by default p2pint will do 10000 initial random steps.
At the end of this calculation you should obtain the result presented in the article.