[Advanced] Nanoparticle energy¶
This section contains advanced content. Those who wish to hurry to the next chapter may skip it and read it later.
In this section, we will try to calculate the excess energy of nanoparticles (cluster structures) and create adsorption structures on supports.
[1]:
import pfp_api_client
from pfp_api_client.pfp.calculators.ase_calculator import ASECalculator
from pfp_api_client.pfp.estimator import Estimator, EstimatorCalcMode
from pfcc_extras.visualize.view import view_ngl
print(f"pfp_api_client: {pfp_api_client.__version__}")
estimator = Estimator(calc_mode=EstimatorCalcMode.PBE, model_version="v8.0.0")
calculator = ASECalculator(estimator)
pfp_api_client: 1.23.1
[2]:
from ase.cluster import Decahedron, Icosahedron, Octahedron, wulff_construction
from ase import Atoms
from ase.build import bulk
from ase.constraints import ExpCellFilter, StrainFilter
from ase.optimize import LBFGS
from ase.io import Trajectory
import numpy as np
import pandas as pd
Excess energy¶
A material that is a pure metal mixed with one or more other elements is called an alloy. The property of metals changes significantly when combining two or more elements.
For example, duralumin, a mixture of aluminum and copper or magnesium, is used in aerospace equipment because of its lightweight and hardness.
A mixture of two elements is called a binary alloy, while a mixture of three or more elements is called a multinary alloy.
Multinary alloys are expected to lead to the discovery of materials with new properties. As the types of elements increase, the combinations of their composition ratios increase, and this is an area that has not yet been analyzed. Matlantis can handle such systems, taking advantage of its versatility.
When considering the atomic structure of these alloys, it is necessary to know how they mix in reality and whether they are combinations that can be mixed in the first place.
Excess energy is a measure of the stability of such alloys. The excess energy of a binary alloy of element A and element B is calculated as follows and indicates how stable the energy of the alloy is compared to the case where elements A and B are not mixed together.
\[E_{\rm{excess}} = \frac{1}{N_{\rm{alloy}}} \left( E_{\rm{alloy}} - \frac{N_{\rm{alloyA}}}{N_{\rm{alloy}}} E_{\rm{A}} - \frac{N_{\rm{alloyB}}}{N_{\rm{alloy}}} E_{\rm{B}} \right)\]
\(E_{\rm{alloy}}\) is the energy of the alloy, \(E_\rm{A}, E_\rm{B}\) is the energy when composed of single elements A or B, and \(N_{\rm{alloy}}, N_{\rm{alloyA}}, N_{\rm{alloyB}}\) are the total number of atoms in the alloy, the number of element A atoms, and the number of element B atoms, respectively.
The same definition can be used for the multinary alloy.
Let us evaluate its stability by evaluating the excess energy for a mixed Pt and Pd structure.
Reference paper:
Electronic Structure and Phase Stability of PdPt Nanoparticles
Electronic structure and phase stability of Pt3M (M = Co, Ni, and Cu) bimetallic nanoparticles
Calculations of Real-System Nanoparticles Using Universal Neural Network Potential PFP
We prepare Pt711 nanoparticle, and mix it with Pd. Even when considering binary nanoparticles, there are various possibilities of how they are mixed. This tutorial will create the following structure and evaluate its excess energy.
Structure in which Pt and Pd are evenly mixed
Structure with Pt in the inner shell and Pd in the outer shell
Structure with Pd in the inner shell and Pt in the outer shell
This is a method definition to create a core shell structure. Feel free to skip the details of this method.
[3]:
from typing import List, Tuple
from ase import Atoms, neighborlist
from ase.cluster import Cluster
import numpy as np
from ase.data import atomic_numbers
def cluster2atoms(cluster: Cluster) -> Atoms:
"""Convert ASE Cluster to ASE Atoms
Args:
cluster (Cluster): input cluster instance
Returns:
atoms (Atoms): converted output, atoms instance
"""
return Atoms(cluster.symbols, cluster.positions, cell=cluster.cell)
def calc_coordination_numbers(atoms: Atoms) -> Tuple[List[int], List[np.ndarray]]:
"""Calculates coordination number
Args:
atoms: input atoms
Returns:
cns (list): coordination number for each atom
bonds (list): bond destination indices for each atom
"""
nl = neighborlist.NeighborList(
neighborlist.natural_cutoffs(atoms), self_interaction=False, bothways=True
)
nl.update(atoms)
bonds = []
cns = []
for i, _ in enumerate(atoms):
indices, offsets = nl.get_neighbors(i)
bonds.append(indices)
cns.append(len(indices))
return cns, bonds
def substitute(scaffold: Atoms, sites: np.ndarray, elements: List[str]) -> Atoms:
"""Substibute `elements` to `sites` indices of `scaffold` atoms
Args:
scaffold (Atoms): Original input atoms
sites (np.ndarray): site indices to substitute `elements`
elements (list): elements to be substituted
Returns:
substituted (Atoms): substituted ase atoms
"""
substituted = scaffold.copy()
for site, element in zip(sites, elements):
substituted.numbers[site] = atomic_numbers[element]
return substituted
def make_core_shell(scaffold: Atoms, element: str) -> Atoms:
"""Make core shell structure
Input `scaffold` element is kept inside core shell,
and outside surface is replaced by `element`.
Note that it is not fully tested.
It was not guaranteed to work on all the cases.
Args:
scaffold (Atoms): input cluster structure
element (str): outside surface element to be replaced
Returns:
coreshell (Atoms): core shell structure
"""
# CN : vertex < edge < surface < core
cn = np.array(calc_coordination_numbers(scaffold)[0])
cn_set = np.unique(cn)
vertexes = None
surfaces = None
cores = None
if len(cn_set) == 1:
pass
elif len(cn_set) == 2:
cores = np.where(cn == cn_set[1])[0]
surfaces = np.where(cn == cn_set[0])[0]
elif len(cn_set) == 3 or len(cn_set) == 4:
cores = np.where(cn == cn_set[-1])[0]
surfaces = np.where(cn != cn_set[-1])[0]
vertexes = np.where(cn == cn_set[0])[0]
else:
cores = np.where(cn == cn_set[-1])[0]
surfaces = np.where(cn != cn_set[-1])[0]
vertexes = np.where(np.isin(cn, cn_set[:-3]))[0]
if surfaces is None:
core_shell = scaffold.copy()
else:
core_shell = substitute(scaffold, surfaces, [element] * len(surfaces))
return core_shell
First, a nanoparticle skeleton structure (scaffold) is created as a base structure.
[4]:
Pt711 = cluster2atoms(Octahedron("Pt", 11, cutoff=4))
view_ngl(Pt711)
[4]:
Create a Pd306Pt405 structure in which only the inner shell of the base skeleton is replaced with “Pd” element using the make_core_shell function.
[5]:
Pd306Pt405 = make_core_shell(Pt711, "Pd")
view_ngl(Pd306Pt405)
[5]:
Similarly, create the Pd405Pt306 structure whose inner shell is Pt and outer shell is Pd.
[6]:
Pd711 = Octahedron("Pd", 11, cutoff=4)
Pd405Pt306 = make_core_shell(Pd711, "Pt")
view_ngl(Pd405Pt306)
[6]:
[7]:
symbols, counts = np.unique(Pd405Pt306.symbols, return_counts=True)
print(f"Pd405Pt306 structure contains {symbols} with counts {counts}", )
symbols, counts = np.unique(Pd306Pt405.symbols, return_counts=True)
print(f"Pd306Pt405 structure contains {symbols} with counts {counts}", )
Pd405Pt306 structure contains ['Pd' 'Pt'] with counts [405 306]
Pd306Pt405 structure contains ['Pd' 'Pt'] with counts [306 405]
Let’s apply structural relaxation for each structure to obtain its energy.
[8]:
from ase.optimize import FIRE
def get_opt_energy(atoms, fmax=0.001):
opt = FIRE(atoms)
opt.run(fmax=fmax)
return atoms.get_total_energy()
[9]:
print("Optimizing Pt711")
Pt711.calc = calculator
E_pt711 = get_opt_energy(Pt711)
print("Optimizing Pd306Pt405")
Pd306Pt405.calc = calculator
E_pd306pt405 = get_opt_energy(Pd306Pt405)
print("Optimizing Pd405Pt306")
Pd405Pt306.calc = calculator
E_pd405pt306 = get_opt_energy(Pd405Pt306)
print("Optimizing Pd711")
Pd711.calc = calculator
E_pd711 = get_opt_energy(Pd711)
Optimizing Pt711
Step Time Energy fmax
FIRE: 0 05:06:26 -3609.569290 1.040004
FIRE: 1 05:06:26 -3610.618085 0.997116
FIRE: 2 05:06:26 -3612.416157 0.909194
FIRE: 3 05:06:26 -3613.983257 0.812325
FIRE: 4 05:06:26 -3615.361402 0.709797
FIRE: 5 05:06:26 -3616.582632 0.603863
FIRE: 6 05:06:27 -3617.676292 0.498381
FIRE: 7 05:06:27 -3618.662917 0.399323
FIRE: 8 05:06:27 -3619.553256 0.339693
FIRE: 9 05:06:27 -3620.347276 0.311894
FIRE: 10 05:06:27 -3621.047967 0.285431
FIRE: 11 05:06:27 -3621.657066 0.239392
FIRE: 12 05:06:27 -3622.182567 0.213061
FIRE: 13 05:06:27 -3622.631155 0.208877
FIRE: 14 05:06:27 -3623.011035 0.195828
FIRE: 15 05:06:27 -3623.328874 0.174904
FIRE: 16 05:06:28 -3623.590156 0.149677
FIRE: 17 05:06:28 -3623.795950 0.130845
FIRE: 18 05:06:28 -3623.951072 0.119098
FIRE: 19 05:06:28 -3624.068673 0.110227
FIRE: 20 05:06:28 -3624.158420 0.120910
FIRE: 21 05:06:28 -3624.221578 0.121859
FIRE: 22 05:06:28 -3624.259647 0.101970
FIRE: 23 05:06:28 -3624.277939 0.124756
FIRE: 24 05:06:29 -3624.355435 0.093453
FIRE: 25 05:06:29 -3624.438236 0.059104
FIRE: 26 05:06:29 -3624.504409 0.046673
FIRE: 27 05:06:29 -3624.540790 0.049031
FIRE: 28 05:06:29 -3624.549812 0.047167
FIRE: 29 05:06:29 -3624.554610 0.040623
FIRE: 30 05:06:29 -3624.562142 0.030064
FIRE: 31 05:06:29 -3624.569143 0.024587
FIRE: 32 05:06:29 -3624.574742 0.025425
FIRE: 33 05:06:29 -3624.578666 0.024004
FIRE: 34 05:06:29 -3624.581829 0.022947
FIRE: 35 05:06:30 -3624.584106 0.019925
FIRE: 36 05:06:30 -3624.585299 0.015150
FIRE: 37 05:06:30 -3624.585321 0.014810
FIRE: 38 05:06:30 -3624.585917 0.014117
FIRE: 39 05:06:30 -3624.586723 0.013142
FIRE: 40 05:06:30 -3624.587187 0.011900
FIRE: 41 05:06:30 -3624.587886 0.010466
FIRE: 42 05:06:30 -3624.588935 0.009258
FIRE: 43 05:06:30 -3624.589417 0.008267
FIRE: 44 05:06:30 -3624.590290 0.007319
FIRE: 45 05:06:31 -3624.590656 0.006103
FIRE: 46 05:06:31 -3624.591165 0.006491
FIRE: 47 05:06:31 -3624.591811 0.006671
FIRE: 48 05:06:31 -3624.592166 0.007046
FIRE: 49 05:06:31 -3624.592468 0.007752
FIRE: 50 05:06:31 -3624.593492 0.008142
FIRE: 51 05:06:31 -3624.594433 0.007817
FIRE: 52 05:06:31 -3624.595124 0.005346
FIRE: 53 05:06:31 -3624.595783 0.005861
FIRE: 54 05:06:31 -3624.596135 0.006223
FIRE: 55 05:06:32 -3624.596072 0.005749
FIRE: 56 05:06:32 -3624.595873 0.004870
FIRE: 57 05:06:32 -3624.596144 0.003680
FIRE: 58 05:06:32 -3624.596099 0.002518
FIRE: 59 05:06:32 -3624.596321 0.002303
FIRE: 60 05:06:32 -3624.596206 0.002044
FIRE: 61 05:06:32 -3624.596292 0.001735
FIRE: 62 05:06:32 -3624.596192 0.001515
FIRE: 63 05:06:32 -3624.596448 0.001490
FIRE: 64 05:06:33 -3624.596260 0.001484
FIRE: 65 05:06:33 -3624.596439 0.001470
FIRE: 66 05:06:33 -3624.596298 0.001456
FIRE: 67 05:06:33 -3624.596388 0.001447
FIRE: 68 05:06:33 -3624.596480 0.001421
FIRE: 69 05:06:33 -3624.596424 0.001405
FIRE: 70 05:06:33 -3624.596384 0.001372
FIRE: 71 05:06:33 -3624.596381 0.001336
FIRE: 72 05:06:33 -3624.596433 0.001274
FIRE: 73 05:06:33 -3624.596414 0.001209
FIRE: 74 05:06:33 -3624.596202 0.001148
FIRE: 75 05:06:33 -3624.596449 0.001080
FIRE: 76 05:06:34 -3624.596358 0.001115
FIRE: 77 05:06:34 -3624.596519 0.001125
FIRE: 78 05:06:34 -3624.596378 0.000971
Optimizing Pd306Pt405
Step Time Energy fmax
FIRE: 0 05:06:34 -3125.594099 0.531633
FIRE: 1 05:06:34 -3125.926152 0.501638
FIRE: 2 05:06:34 -3126.506870 0.442726
FIRE: 3 05:06:34 -3127.202026 0.357763
FIRE: 4 05:06:34 -3127.886976 0.253067
FIRE: 5 05:06:34 -3128.431623 0.208540
FIRE: 6 05:06:34 -3128.884657 0.214499
FIRE: 7 05:06:35 -3129.273722 0.217996
FIRE: 8 05:06:35 -3129.607956 0.177662
FIRE: 9 05:06:35 -3129.881719 0.119569
FIRE: 10 05:06:35 -3130.089639 0.141494
FIRE: 11 05:06:35 -3130.239066 0.127599
FIRE: 12 05:06:35 -3130.343764 0.107444
FIRE: 13 05:06:35 -3130.408191 0.105237
FIRE: 14 05:06:35 -3130.430606 0.081156
FIRE: 15 05:06:35 -3130.444893 0.076541
FIRE: 16 05:06:36 -3130.469668 0.068947
FIRE: 17 05:06:36 -3130.497958 0.059786
FIRE: 18 05:06:36 -3130.526015 0.048124
FIRE: 19 05:06:36 -3130.550095 0.042873
FIRE: 20 05:06:36 -3130.570362 0.050978
FIRE: 21 05:06:36 -3130.586748 0.050684
FIRE: 22 05:06:36 -3130.599216 0.040290
FIRE: 23 05:06:36 -3130.606180 0.026648
FIRE: 24 05:06:36 -3130.608459 0.028279
FIRE: 25 05:06:37 -3130.608876 0.027669
FIRE: 26 05:06:37 -3130.610401 0.026463
FIRE: 27 05:06:37 -3130.612210 0.024709
FIRE: 28 05:06:37 -3130.614231 0.022467
FIRE: 29 05:06:37 -3130.616692 0.019835
FIRE: 30 05:06:37 -3130.618739 0.018257
FIRE: 31 05:06:37 -3130.621115 0.019769
FIRE: 32 05:06:37 -3130.622977 0.020521
FIRE: 33 05:06:37 -3130.625344 0.020089
FIRE: 34 05:06:37 -3130.627259 0.018179
FIRE: 35 05:06:37 -3130.629322 0.014800
FIRE: 36 05:06:38 -3130.630452 0.010544
FIRE: 37 05:06:38 -3130.631953 0.010931
FIRE: 38 05:06:38 -3130.633008 0.011222
FIRE: 39 05:06:38 -3130.634638 0.011352
FIRE: 40 05:06:38 -3130.636388 0.011728
FIRE: 41 05:06:38 -3130.638124 0.012170
FIRE: 42 05:06:38 -3130.639831 0.012997
FIRE: 43 05:06:38 -3130.640126 0.007894
FIRE: 44 05:06:38 -3130.640162 0.006968
FIRE: 45 05:06:39 -3130.640492 0.006198
FIRE: 46 05:06:39 -3130.640475 0.006515
FIRE: 47 05:06:39 -3130.640574 0.006386
FIRE: 48 05:06:39 -3130.640730 0.005500
FIRE: 49 05:06:39 -3130.640497 0.003782
FIRE: 50 05:06:39 -3130.640700 0.002904
FIRE: 51 05:06:39 -3130.640720 0.002245
FIRE: 52 05:06:39 -3130.640654 0.002160
FIRE: 53 05:06:39 -3130.640812 0.002023
FIRE: 54 05:06:39 -3130.640926 0.001795
FIRE: 55 05:06:40 -3130.640969 0.001520
FIRE: 56 05:06:40 -3130.641039 0.001206
FIRE: 57 05:06:40 -3130.640825 0.001088
FIRE: 58 05:06:40 -3130.640900 0.000958
Optimizing Pd405Pt306
Step Time Energy fmax
FIRE: 0 05:06:40 -2936.142464 0.854851
FIRE: 1 05:06:40 -2937.220114 0.826394
FIRE: 2 05:06:40 -2938.999905 0.768947
FIRE: 3 05:06:40 -2940.498574 0.705648
FIRE: 4 05:06:40 -2941.772741 0.635854
FIRE: 5 05:06:41 -2942.872919 0.560104
FIRE: 6 05:06:41 -2943.835201 0.480506
FIRE: 7 05:06:41 -2944.687657 0.399513
FIRE: 8 05:06:41 -2945.450229 0.318803
FIRE: 9 05:06:41 -2946.133509 0.280909
FIRE: 10 05:06:41 -2946.739569 0.241686
FIRE: 11 05:06:41 -2947.267283 0.196206
FIRE: 12 05:06:41 -2947.715539 0.165348
FIRE: 13 05:06:42 -2948.083806 0.153118
FIRE: 14 05:06:42 -2948.375531 0.137163
FIRE: 15 05:06:42 -2948.598662 0.121425
FIRE: 16 05:06:42 -2948.762756 0.124072
FIRE: 17 05:06:42 -2948.876736 0.126385
FIRE: 18 05:06:42 -2948.951986 0.112937
FIRE: 19 05:06:42 -2948.998015 0.109445
FIRE: 20 05:06:42 -2949.021608 0.111756
FIRE: 21 05:06:42 -2949.079012 0.103268
FIRE: 22 05:06:43 -2949.161898 0.082761
FIRE: 23 05:06:43 -2949.237292 0.082829
FIRE: 24 05:06:43 -2949.295640 0.089292
FIRE: 25 05:06:43 -2949.334601 0.062579
FIRE: 26 05:06:43 -2949.351760 0.056082
FIRE: 27 05:06:43 -2949.353941 0.052316
FIRE: 28 05:06:43 -2949.358608 0.045132
FIRE: 29 05:06:43 -2949.364378 0.035212
FIRE: 30 05:06:43 -2949.370473 0.030386
FIRE: 31 05:06:43 -2949.376524 0.028407
FIRE: 32 05:06:43 -2949.382239 0.026030
FIRE: 33 05:06:43 -2949.386982 0.023332
FIRE: 34 05:06:44 -2949.392044 0.020129
FIRE: 35 05:06:44 -2949.396432 0.020099
FIRE: 36 05:06:44 -2949.400091 0.021226
FIRE: 37 05:06:44 -2949.404231 0.020055
FIRE: 38 05:06:44 -2949.409252 0.018011
FIRE: 39 05:06:44 -2949.413977 0.014953
FIRE: 40 05:06:44 -2949.418989 0.015857
FIRE: 41 05:06:44 -2949.423180 0.019960
FIRE: 42 05:06:44 -2949.424781 0.013920
FIRE: 43 05:06:44 -2949.424999 0.012877
FIRE: 44 05:06:44 -2949.425377 0.010904
FIRE: 45 05:06:45 -2949.425272 0.008241
FIRE: 46 05:06:45 -2949.425685 0.005244
FIRE: 47 05:06:45 -2949.426045 0.005063
FIRE: 48 05:06:45 -2949.425682 0.005181
FIRE: 49 05:06:45 -2949.426244 0.005148
FIRE: 50 05:06:45 -2949.425904 0.004175
FIRE: 51 05:06:45 -2949.426189 0.004060
FIRE: 52 05:06:45 -2949.426053 0.003837
FIRE: 53 05:06:45 -2949.425944 0.003512
FIRE: 54 05:06:46 -2949.425973 0.003111
FIRE: 55 05:06:46 -2949.425993 0.002623
FIRE: 56 05:06:46 -2949.426294 0.002099
FIRE: 57 05:06:46 -2949.426012 0.001557
FIRE: 58 05:06:46 -2949.426477 0.001123
FIRE: 59 05:06:46 -2949.426254 0.001141
FIRE: 60 05:06:46 -2949.426264 0.001393
FIRE: 61 05:06:46 -2949.426410 0.001671
FIRE: 62 05:06:46 -2949.426095 0.001751
FIRE: 63 05:06:46 -2949.426225 0.001728
FIRE: 64 05:06:46 -2949.426248 0.001679
FIRE: 65 05:06:47 -2949.426392 0.001608
FIRE: 66 05:06:47 -2949.426136 0.001516
FIRE: 67 05:06:47 -2949.426391 0.001404
FIRE: 68 05:06:47 -2949.426468 0.001275
FIRE: 69 05:06:47 -2949.426149 0.001135
FIRE: 70 05:06:47 -2949.426182 0.000965
Optimizing Pd711
Step Time Energy fmax
FIRE: 0 05:06:47 -2422.823697 0.360904
FIRE: 1 05:06:47 -2423.073756 0.333712
FIRE: 2 05:06:47 -2423.507992 0.304226
FIRE: 3 05:06:47 -2424.031505 0.272105
FIRE: 4 05:06:48 -2424.555334 0.229604
FIRE: 5 05:06:48 -2425.033977 0.189223
FIRE: 6 05:06:48 -2425.436250 0.208382
FIRE: 7 05:06:48 -2425.784118 0.192289
FIRE: 8 05:06:48 -2426.085797 0.151484
FIRE: 9 05:06:48 -2426.335914 0.115907
FIRE: 10 05:06:48 -2426.531106 0.128541
FIRE: 11 05:06:48 -2426.676634 0.120186
FIRE: 12 05:06:48 -2426.782396 0.104547
FIRE: 13 05:06:49 -2426.854633 0.113271
FIRE: 14 05:06:49 -2426.894728 0.094800
FIRE: 15 05:06:49 -2426.904727 0.084601
FIRE: 16 05:06:49 -2426.917991 0.075479
FIRE: 17 05:06:49 -2426.940463 0.063126
FIRE: 18 05:06:49 -2426.967530 0.059500
FIRE: 19 05:06:49 -2426.992471 0.053825
FIRE: 20 05:06:49 -2427.013807 0.047062
FIRE: 21 05:06:49 -2427.030480 0.049089
FIRE: 22 05:06:50 -2427.044643 0.046383
FIRE: 23 05:06:50 -2427.056723 0.045267
FIRE: 24 05:06:50 -2427.065122 0.029118
FIRE: 25 05:06:50 -2427.068324 0.029192
FIRE: 26 05:06:50 -2427.068814 0.027890
FIRE: 27 05:06:50 -2427.069915 0.025382
FIRE: 28 05:06:50 -2427.070843 0.021859
FIRE: 29 05:06:50 -2427.072794 0.017589
FIRE: 30 05:06:50 -2427.073930 0.015989
FIRE: 31 05:06:51 -2427.075962 0.014601
FIRE: 32 05:06:51 -2427.077286 0.013146
FIRE: 33 05:06:51 -2427.078323 0.012604
FIRE: 34 05:06:51 -2427.079718 0.012204
FIRE: 35 05:06:51 -2427.081257 0.009762
FIRE: 36 05:06:51 -2427.082506 0.010402
FIRE: 37 05:06:51 -2427.082643 0.010911
FIRE: 38 05:06:51 -2427.083651 0.008835
FIRE: 39 05:06:51 -2427.083637 0.009758
FIRE: 40 05:06:52 -2427.084294 0.009453
FIRE: 41 05:06:52 -2427.085559 0.008523
FIRE: 42 05:06:52 -2427.085955 0.010269
FIRE: 43 05:06:52 -2427.087267 0.008518
FIRE: 44 05:06:52 -2427.087216 0.005742
FIRE: 45 05:06:52 -2427.087116 0.004991
FIRE: 46 05:06:52 -2427.087314 0.003645
FIRE: 47 05:06:52 -2427.087510 0.003000
FIRE: 48 05:06:52 -2427.087539 0.002685
FIRE: 49 05:06:52 -2427.087881 0.003552
FIRE: 50 05:06:53 -2427.087747 0.003360
FIRE: 51 05:06:53 -2427.087616 0.002194
FIRE: 52 05:06:53 -2427.088008 0.001295
FIRE: 53 05:06:53 -2427.088111 0.002169
FIRE: 54 05:06:53 -2427.088089 0.002303
FIRE: 55 05:06:53 -2427.087774 0.001213
FIRE: 56 05:06:53 -2427.088140 0.001116
FIRE: 57 05:06:53 -2427.088103 0.001009
FIRE: 58 05:06:53 -2427.088123 0.000960
We can now calculate excess energy from these energies.
[10]:
E_exess_pd306pt405 = (E_pd306pt405 - 306 / 711 * E_pd711 - 405 / 711 * E_pt711) / 711
E_exess_pd405pt306 = (E_pd405pt306 - 405 / 711 * E_pd711 - 306 / 711 * E_pt711) / 711
print(f"Excess energy of Pd306Pt405 = {E_exess_pd306pt405 * 1000:.2f} meV")
print(f"Excess energy of Pd405Pt306 = {E_exess_pd405pt306 * 1000:.2f} meV")
Excess energy of Pd306Pt405 = -30.14 meV
Excess energy of Pd405Pt306 = -9.78 meV
It suggests that Pd306Pt405, which has a negative Excess energy, is more stable when mixed than when Pd and Pt nanoparticles exist alone. On the other hand, the Pd405Pt306 structure is more unstable than Pd306Pt405.
From this result, we can consider that in Pd-Pt alloy particles, a structure in which Pd is in the outer shell is likely to be stable in nature.
Finally, let us find the excess energy of a structure with 306 Pt and 405 Pd randomly arranged.
[11]:
Pd405Pt306_random = Pt711.copy()
# randomly choose 405 atoms to be replaced to Pd
pd_indices = np.random.choice(np.arange(711), 405, replace=False)
Pd405Pt306_random.numbers[pd_indices] = atomic_numbers["Pd"]
print(f"Replaced to Pd with indices {pd_indices}")
view_ngl(Pd405Pt306_random)
Replaced to Pd with indices [557 262 313 188 247 15 220 678 208 53 494 278 384 301 350 168 619 425
60 245 123 603 45 594 346 638 516 89 404 559 9 334 182 476 394 525
622 501 221 503 118 106 120 642 698 171 347 423 397 355 0 561 39 543
196 82 377 645 170 183 222 625 595 502 169 291 211 2 156 530 600 545
518 692 44 686 424 8 510 623 632 379 212 386 409 531 43 57 635 442
263 290 460 296 214 505 242 679 75 639 36 145 136 246 283 259 337 508
288 544 71 491 612 321 429 703 343 55 511 272 64 710 658 327 422 200
624 489 708 497 426 583 352 63 656 467 325 226 537 215 174 473 4 433
646 563 108 615 668 388 199 688 702 270 341 382 587 536 441 495 474 651
150 435 618 370 565 428 192 96 661 165 611 269 655 12 677 34 202 461
306 224 90 427 414 223 459 94 228 3 693 504 683 593 398 597 447 408
187 637 97 665 339 621 67 672 237 328 332 164 177 193 59 191 311 111
670 19 469 641 419 134 371 430 402 74 66 573 261 329 130 614 574 244
47 472 119 393 493 584 268 417 450 631 648 99 207 216 455 176 304 418
378 68 517 581 629 556 550 17 186 604 107 345 360 519 650 138 73 310
636 27 294 206 167 28 488 401 499 369 526 514 218 232 7 500 528 62
308 303 575 297 571 273 552 131 687 385 81 392 353 161 69 84 54 383
309 24 399 436 527 569 240 243 10 126 373 653 236 257 660 13 295 101
451 153 674 65 707 33 694 406 669 319 634 659 478 372 286 1 258 152
358 453 160 521 381 415 40 52 32 652 689 287 452 463 116 482 485 127
567 676 178 264 496 522 367 155 564 159 413 317 671 180 354 146 443 462
103 255 76 87 331 326 533 282 133 534 602 490 626 241 172 78 175 579
209 590 681 541 132 194 70 157 48]
[11]:
[12]:
print("Optimizing Pd405Pt306_random")
Pd405Pt306_random.calc = calculator
E_pd405pt306_random = get_opt_energy(Pd405Pt306_random)
Optimizing Pd405Pt306_random
Step Time Energy fmax
FIRE: 0 05:06:54 -2951.463955 0.686472
FIRE: 1 05:06:54 -2951.883058 0.655774
FIRE: 2 05:06:54 -2952.612842 0.597436
FIRE: 3 05:06:54 -2953.475407 0.512045
FIRE: 4 05:06:54 -2954.220137 0.405601
FIRE: 5 05:06:54 -2954.781796 0.287330
FIRE: 6 05:06:54 -2955.206977 0.279969
FIRE: 7 05:06:54 -2955.536052 0.267057
FIRE: 8 05:06:54 -2955.794894 0.215046
FIRE: 9 05:06:54 -2955.996466 0.194621
FIRE: 10 05:06:54 -2956.149418 0.202107
FIRE: 11 05:06:55 -2956.267670 0.195909
FIRE: 12 05:06:55 -2956.365972 0.174524
FIRE: 13 05:06:55 -2956.449970 0.176056
FIRE: 14 05:06:55 -2956.515675 0.163480
FIRE: 15 05:06:55 -2956.559975 0.171774
FIRE: 16 05:06:55 -2956.589479 0.164634
FIRE: 17 05:06:55 -2956.639216 0.150769
FIRE: 18 05:06:55 -2956.693862 0.130952
FIRE: 19 05:06:55 -2956.742611 0.106435
FIRE: 20 05:06:55 -2956.779987 0.079620
FIRE: 21 05:06:55 -2956.806685 0.056871
FIRE: 22 05:06:56 -2956.823439 0.051401
FIRE: 23 05:06:56 -2956.833863 0.057812
FIRE: 24 05:06:56 -2956.836509 0.065774
FIRE: 25 05:06:56 -2956.838056 0.063241
FIRE: 26 05:06:56 -2956.840871 0.058339
FIRE: 27 05:06:56 -2956.844654 0.051365
FIRE: 28 05:06:56 -2956.849296 0.042768
FIRE: 29 05:06:56 -2956.853617 0.035873
FIRE: 30 05:06:56 -2956.857245 0.033567
FIRE: 31 05:06:56 -2956.860880 0.031002
FIRE: 32 05:06:57 -2956.864675 0.027350
FIRE: 33 05:06:57 -2956.867384 0.022381
FIRE: 34 05:06:57 -2956.870122 0.021284
FIRE: 35 05:06:57 -2956.872151 0.018652
FIRE: 36 05:06:57 -2956.874154 0.020530
FIRE: 37 05:06:57 -2956.875844 0.022471
FIRE: 38 05:06:57 -2956.877792 0.021527
FIRE: 39 05:06:57 -2956.880602 0.023119
FIRE: 40 05:06:57 -2956.883679 0.022468
FIRE: 41 05:06:57 -2956.887104 0.019191
FIRE: 42 05:06:57 -2956.890437 0.013375
FIRE: 43 05:06:58 -2956.892346 0.012415
FIRE: 44 05:06:58 -2956.892579 0.011058
FIRE: 45 05:06:58 -2956.892868 0.009238
FIRE: 46 05:06:58 -2956.893189 0.007834
FIRE: 47 05:06:58 -2956.893483 0.006969
FIRE: 48 05:06:58 -2956.893334 0.007206
FIRE: 49 05:06:58 -2956.893595 0.007273
FIRE: 50 05:06:58 -2956.893736 0.006222
FIRE: 51 05:06:58 -2956.894191 0.005410
FIRE: 52 05:06:58 -2956.893971 0.006673
FIRE: 53 05:06:59 -2956.894060 0.006728
FIRE: 54 05:06:59 -2956.894351 0.005678
FIRE: 55 05:06:59 -2956.894622 0.004578
FIRE: 56 05:06:59 -2956.894916 0.006321
FIRE: 57 05:06:59 -2956.895574 0.004792
FIRE: 58 05:06:59 -2956.895868 0.005141
FIRE: 59 05:06:59 -2956.896080 0.004266
FIRE: 60 05:06:59 -2956.896043 0.004952
FIRE: 61 05:06:59 -2956.896294 0.004693
FIRE: 62 05:06:59 -2956.896478 0.004576
FIRE: 63 05:07:00 -2956.896783 0.002752
FIRE: 64 05:07:00 -2956.896877 0.002213
FIRE: 65 05:07:00 -2956.896871 0.003885
FIRE: 66 05:07:00 -2956.896523 0.003477
FIRE: 67 05:07:00 -2956.896561 0.002706
FIRE: 68 05:07:00 -2956.896907 0.001703
FIRE: 69 05:07:00 -2956.896514 0.001313
FIRE: 70 05:07:00 -2956.896905 0.001457
FIRE: 71 05:07:00 -2956.896486 0.001937
FIRE: 72 05:07:01 -2956.896520 0.002071
FIRE: 73 05:07:01 -2956.896531 0.001899
FIRE: 74 05:07:01 -2956.896908 0.001363
FIRE: 75 05:07:01 -2956.896635 0.000957
[13]:
view_ngl(Pd405Pt306_random)
[13]:
[14]:
E_exess_pd405pt306_random = (E_pd405pt306_random - 405 / 711 * E_pd711 - 306 / 711 * E_pt711) / 711
print(f"Excess energy of Pd306Pt405 random = {E_exess_pd405pt306_random * 1000:.2f} meV")
Excess energy of Pd306Pt405 random = -20.29 meV
Again, negative excess energy is obtained, indicating that this structure can be stable.
In this case, the structure was created using a completely random configuration, but in reality, when substances are mixed, it may be possible to create a more stable structure by taking a localized pattern. Monte Carlo methods are often used to optimize the placement patterns in this type of analysis, but it is omitted here. (A description of the Monte Carlo method and examples may be provided later in the future.)
Thus, by creating various structures and calculating their excess energy, it is possible to analyze what the stable structure of the alloy will be.
Adsorption structure of nanoparticles on the support¶
This tutorial will only present a simple computational example of modeling adsorption on a support, and will not attempt to validate this structure in reality.
In this tutorial, we will use SnO2 as noble metal support and Pt as a nanoparticle to create a structure in which a Pt nanoparticle is placed on the support.
[15]:
# bulk, support material
from ase.io import read
SnO2 = read("../input/SnO2_mp-856_conventional_standard.cif")
view_ngl(SnO2, representations=["ball+stick"])
[15]:
Here we use pymatgen’s SlabGenerator to create the slab structure (cut out specific mirror faces from the bulk). This is done by specifying the parameters of the slab structure to be created as initialization parameters when instantiating the SlabGenerator. By calling the get_slabs method, you will get a list of slab structures that match the specified initialization parameters.
More information is also available in the following Materials Project Workshop.
[16]:
# Generate slab
from ase.build import make_supercell
import numpy as np
from pymatgen.core.surface import SlabGenerator
from pymatgen.io.ase import AseAtomsAdaptor
slab_gen = SlabGenerator(
initial_structure=AseAtomsAdaptor.get_structure(SnO2),
miller_index=[1,1,0],
min_slab_size=5.0, # ここで層の出方が変わる
min_vacuum_size=15.0, # nanoparticleを載せるので大きめに
lll_reduce=False,
center_slab=True,
primitive=True,
max_normal_search=1,
)
slabs = slab_gen.get_slabs(tol=0.3, bonds=None, max_broken_bonds=0, symmetrize=False)
The resulting slabs are pymatgen instances. It can be converted to an ASE Atoms instance using AseAtomsAdaptor.
The obtained structure is converted to ASE Atoms and visualized.
[17]:
slab_atoms_list = [AseAtomsAdaptor.get_atoms(slab) for slab in slabs]
view_ngl(slab_atoms_list, representations=["ball+stick"])
[17]:
Two structures were obtained.
In the following sections, we will use the second structure to create a slab. After creating the supercell in ASE, the height of the lowest atom (layer) is set to 0 by translating in the z-axis direction.
[18]:
slab = slab_atoms_list[1].copy()
# make supercell: expand to xy-plane
#slab = make_supercell(slab, [[4, 0, 0], [0, 2, 0], [0, 0, 1]]) # this is same with below.
slab = slab * (4, 2, 1)
# shift `slab` to bottom of cell
min_pos_z = np.min(slab.positions, axis=0)[2]
slab.set_positions(slab.positions - [0, 0, min_pos_z])
[19]:
view_ngl(slab, representations=["ball+stick"], replace_structure=True)
[19]:
We created a slab structure for support.
Next, we create a nanoparticle cluster to be placed on this support.
[20]:
Pt55 = Octahedron("Pt", 5, cutoff=2)
# cut cluster to make half-sphere
cluster = Pt55.copy()
# Rotate cluster to make triangle surface comes to top.
cluster.rotate([0, 0, 1], [1, 1, 1], center=cluster.get_center_of_mass())
# Cut bottom 2 layers
for _ in range(2):
target = np.round(cluster.positions, decimals=0)
del cluster[np.where(target[:,2]==np.min(target[:,2]))[0]]
[21]:
view_ngl(cluster, representations=["ball+stick"])
[21]:
Place the nanoparticle cluster on the support.
Here, the nanoparticle is placed on the middle of the support by a program, but you can also use the SurfaceEditor introduced in chapter 5 to create the initial structure by moving the nanoparticle interactively on GUI.
[22]:
from ase.data import atomic_numbers, chemical_symbols, covalent_radii
# Put Pt37 on top of SnO2. Both perpendincular lines goes z-axis.
slab_xy_size = np.min(slab.cell.cellpar()[0:2])
cluster_xy_size = np.max(
(np.max(cluster.positions, axis=0) - np.min(cluster.positions, axis=0))[0:2]
)
# Vacuum size
min_slab_xy_size = cluster_xy_size + 15
for i in range(1, 5):
print(f"i={i}")
if slab_xy_size * i < min_slab_xy_size:
pass
else:
slab_sc = make_supercell(slab, [[i, 0, 0], [0, i, 0], [0, 0, 1]])
break
slab_surface_xy_center = np.append(
slab_sc.cell.cellpar()[0:2] / 2, np.max(slab_sc.positions, axis=0)[2]
)
cluster_surface_xy_center = np.append(
np.mean(cluster.positions, axis=0)[0:2], np.min(cluster.positions, axis=0)[2]
)
cluster = Atoms(cluster.get_chemical_symbols(), cluster.positions - cluster_surface_xy_center)
slab_surface_covalent_radii = covalent_radii[
slab_sc.get_atomic_numbers()[np.argmax(slab_sc.positions, axis=0)[2]]
]
cluster_surface_covalent_radii = covalent_radii[
cluster.get_atomic_numbers()[np.argmin(cluster.positions, axis=0)[2]]
]
cluster.translate(
slab_surface_xy_center + [0, 0, slab_surface_covalent_radii + cluster_surface_covalent_radii]
)
supported = slab_sc.copy()
supported += cluster
i=1
i=2
[23]:
view_ngl(supported, representations=["ball+stick"])
[23]:
[24]:
import pfp_api_client
from pfp_api_client.pfp.calculators.ase_calculator import ASECalculator
from pfp_api_client.pfp.estimator import Estimator, EstimatorCalcMode
from ase.optimize import BFGS, LBFGS, FIRE
from ase.io import Trajectory
print(f"pfp_api_client: {pfp_api_client.__version__}")
estimator = Estimator(calc_mode=EstimatorCalcMode.PBE_U, model_version="v8.0.0")
calculator = ASECalculator(estimator)
supported.calc = calculator
traj = Trajectory("./SnO2_Pt119.traj", "w", supported)
opt = FIRE(supported)
opt.attach(traj.write, interval=1)
opt.run(fmax=0.005)
traj.close()
pfp_api_client: 1.23.1
Step Time Energy fmax
FIRE: 0 05:07:02 -1856.170263 2.665578
FIRE: 1 05:07:02 -1862.262675 2.242122
FIRE: 2 05:07:02 -1867.449870 2.009662
FIRE: 3 05:07:02 -1871.758847 1.937803
FIRE: 4 05:07:02 -1875.235394 1.854351
FIRE: 5 05:07:02 -1877.972361 1.756824
FIRE: 6 05:07:02 -1880.108393 1.642316
FIRE: 7 05:07:02 -1881.825760 1.508070
FIRE: 8 05:07:02 -1883.341446 1.353713
FIRE: 9 05:07:02 -1884.849230 1.303777
FIRE: 10 05:07:02 -1886.443856 1.201917
FIRE: 11 05:07:03 -1888.094835 0.987404
FIRE: 12 05:07:03 -1889.686761 0.971872
FIRE: 13 05:07:03 -1891.098209 0.956527
FIRE: 14 05:07:03 -1892.274196 0.917137
FIRE: 15 05:07:03 -1893.250302 0.917339
FIRE: 16 05:07:03 -1894.129911 1.004214
FIRE: 17 05:07:03 -1895.013647 1.092757
FIRE: 18 05:07:03 -1895.940917 1.175548
FIRE: 19 05:07:03 -1896.872013 1.233957
FIRE: 20 05:07:03 -1897.722148 1.252479
FIRE: 21 05:07:03 -1898.419551 1.221698
FIRE: 22 05:07:03 -1898.950705 1.139072
FIRE: 23 05:07:04 -1899.368507 1.014610
FIRE: 24 05:07:04 -1899.740725 0.816489
FIRE: 25 05:07:04 -1900.097960 0.519997
FIRE: 26 05:07:04 -1900.418936 0.427894
FIRE: 27 05:07:04 -1900.666274 0.580771
FIRE: 28 05:07:04 -1900.841934 0.872977
FIRE: 29 05:07:04 -1900.999616 0.969969
FIRE: 30 05:07:04 -1901.182197 0.913152
FIRE: 31 05:07:04 -1901.366238 0.619061
FIRE: 32 05:07:04 -1901.500156 0.547311
FIRE: 33 05:07:04 -1901.597105 0.638849
FIRE: 34 05:07:04 -1901.703571 0.638583
FIRE: 35 05:07:05 -1901.812396 0.534441
FIRE: 36 05:07:05 -1901.872484 0.688772
FIRE: 37 05:07:05 -1901.995474 0.906043
FIRE: 38 05:07:05 -1902.037921 0.632184
FIRE: 39 05:07:05 -1902.096061 0.343188
FIRE: 40 05:07:05 -1902.118179 0.150365
FIRE: 41 05:07:05 -1902.121692 0.127778
FIRE: 42 05:07:05 -1902.127382 0.099333
FIRE: 43 05:07:05 -1902.133649 0.099688
FIRE: 44 05:07:05 -1902.139503 0.100180
FIRE: 45 05:07:05 -1902.145153 0.100802
FIRE: 46 05:07:05 -1902.151803 0.101519
FIRE: 47 05:07:06 -1902.159854 0.102313
FIRE: 48 05:07:06 -1902.170347 0.103250
FIRE: 49 05:07:06 -1902.182006 0.104338
FIRE: 50 05:07:06 -1902.193443 0.105569
FIRE: 51 05:07:06 -1902.205230 0.106905
FIRE: 52 05:07:06 -1902.218620 0.108270
FIRE: 53 05:07:06 -1902.232278 0.109647
FIRE: 54 05:07:06 -1902.245239 0.110953
FIRE: 55 05:07:06 -1902.259210 0.111549
FIRE: 56 05:07:06 -1902.274654 0.110601
FIRE: 57 05:07:06 -1902.292077 0.108556
FIRE: 58 05:07:06 -1902.313556 0.106564
FIRE: 59 05:07:07 -1902.339022 0.102928
FIRE: 60 05:07:07 -1902.369553 0.096015
FIRE: 61 05:07:07 -1902.403737 0.087521
FIRE: 62 05:07:07 -1902.441864 0.127309
FIRE: 63 05:07:07 -1902.480308 0.262127
FIRE: 64 05:07:07 -1902.489249 0.552484
FIRE: 65 05:07:07 -1902.546538 0.125462
FIRE: 66 05:07:07 -1902.548483 0.125572
FIRE: 67 05:07:07 -1902.551481 0.125704
FIRE: 68 05:07:07 -1902.554729 0.125682
FIRE: 69 05:07:07 -1902.558526 0.125287
FIRE: 70 05:07:07 -1902.563782 0.124341
FIRE: 71 05:07:07 -1902.570344 0.122752
FIRE: 72 05:07:07 -1902.577610 0.120500
FIRE: 73 05:07:07 -1902.585920 0.117343
FIRE: 74 05:07:08 -1902.596410 0.113322
FIRE: 75 05:07:08 -1902.609888 0.108598
FIRE: 76 05:07:08 -1902.626009 0.110980
FIRE: 77 05:07:08 -1902.646351 0.125224
FIRE: 78 05:07:08 -1902.672708 0.141231
FIRE: 79 05:07:08 -1902.706629 0.158127
FIRE: 80 05:07:08 -1902.752187 0.157374
FIRE: 81 05:07:08 -1902.813123 0.168110
FIRE: 82 05:07:08 -1902.893730 0.157536
FIRE: 83 05:07:08 -1902.993544 0.183617
FIRE: 84 05:07:08 -1903.089208 0.206657
FIRE: 85 05:07:09 -1903.183625 0.207540
FIRE: 86 05:07:09 -1903.276750 0.193371
FIRE: 87 05:07:09 -1903.364973 0.191780
FIRE: 88 05:07:09 -1903.429932 0.177726
FIRE: 89 05:07:09 -1903.459781 0.237578
FIRE: 90 05:07:09 -1903.471484 0.145258
FIRE: 91 05:07:09 -1903.486317 0.109691
FIRE: 92 05:07:09 -1903.496796 0.146517
FIRE: 93 05:07:09 -1903.507670 0.181363
FIRE: 94 05:07:09 -1903.515630 0.167505
FIRE: 95 05:07:09 -1903.526061 0.137261
FIRE: 96 05:07:09 -1903.537515 0.096263
FIRE: 97 05:07:09 -1903.549348 0.075398
FIRE: 98 05:07:10 -1903.562992 0.101925
FIRE: 99 05:07:10 -1903.577643 0.153720
FIRE: 100 05:07:10 -1903.587584 0.090648
FIRE: 101 05:07:10 -1903.585780 0.117460
FIRE: 102 05:07:10 -1903.588151 0.091638
FIRE: 103 05:07:10 -1903.591322 0.088607
FIRE: 104 05:07:10 -1903.593200 0.089134
FIRE: 105 05:07:10 -1903.593538 0.089907
FIRE: 106 05:07:10 -1903.593674 0.089956
FIRE: 107 05:07:10 -1903.594118 0.090052
FIRE: 108 05:07:10 -1903.594602 0.090202
FIRE: 109 05:07:10 -1903.595166 0.090401
FIRE: 110 05:07:10 -1903.595725 0.090647
FIRE: 111 05:07:11 -1903.596297 0.090951
FIRE: 112 05:07:11 -1903.596894 0.091304
FIRE: 113 05:07:11 -1903.597512 0.091748
FIRE: 114 05:07:11 -1903.598348 0.092302
FIRE: 115 05:07:11 -1903.599377 0.092970
FIRE: 116 05:07:11 -1903.600752 0.093768
FIRE: 117 05:07:11 -1903.602551 0.094725
FIRE: 118 05:07:11 -1903.604673 0.095912
FIRE: 119 05:07:11 -1903.607214 0.098675
FIRE: 120 05:07:11 -1903.610187 0.101455
FIRE: 121 05:07:11 -1903.613999 0.103958
FIRE: 122 05:07:11 -1903.618875 0.109311
FIRE: 123 05:07:11 -1903.624811 0.115539
FIRE: 124 05:07:11 -1903.632141 0.122548
FIRE: 125 05:07:12 -1903.641540 0.130080
FIRE: 126 05:07:12 -1903.653040 0.137014
FIRE: 127 05:07:12 -1903.667451 0.147126
FIRE: 128 05:07:12 -1903.685221 0.152102
FIRE: 129 05:07:12 -1903.705488 0.121521
FIRE: 130 05:07:12 -1903.726903 0.110721
FIRE: 131 05:07:12 -1903.749299 0.122232
FIRE: 132 05:07:12 -1903.772122 0.124668
FIRE: 133 05:07:12 -1903.790009 0.157177
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[25]:
SnO2_Pt119 = Trajectory("./SnO2_Pt119.traj")
view_ngl(SnO2_Pt119, representations=["ball+stick"])
[25]:
[26]:
from ase.io import write
from IPython.display import Image
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
write("output/sno2_pt119_opt.png", SnO2_Pt119[-1], rotation="-90x,0y,0z")
fig, ax = plt.subplots(1, 1, figsize=(5, 5))
ax.imshow(mpimg.imread("output/sno2_pt119_opt.png"))
ax.set_axis_off()
ax.set_title("SnO2 - Pt119 optimized structure")
fig.show()
In this way, we were able to create a nanoparticle structure on the support.
Here we can also visualize charge as shown in the paper. We can see that the charge deviates from 0 only near the adsorption surface of the nanoparticle, and the outside of the shell is positive and the inside is negative.
[27]:
v = view_ngl(SnO2_Pt119[-1], show_charge=True)
v.show_charge_label()
v
[27]:
Thus, we were able to create a structure in which Pt nanoparticles are adsorbed on a SnO2 support.
In practice, it is necessary to verify whether this structure is really correct (e.g., whether Pt nanoparticles are adsorbed as fine particles, or whether it is more stable to be adsorbed in a form that stretches homogeneously over the entire surface), but this is out of scope of this tutorial.
By creating such a structure, it is possible to further develop the simulation of
Reactions under catalysts with various surfaces exposed
Reactions at the interface between catalyst and substrate
etc., in combination with the reaction searches and MDs, which will be discussed later.
This allows us to simulate catalytic reactions in a more realistic condition.
Reference
Calculations of Real-System Nanoparticles Using Universal Neural Network Potential PFP
Structural Stability of Ruthenium Nanoparticles: A Density Functional Theory Study
Electronic Structure and Phase Stability of PdPt Nanoparticles
Electronic structure and phase stability of Pt3M (M = Co, Ni, and Cu) bimetallic nanoparticles