[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.CRYSTAL, model_version="latest")
estimator = Estimator(calc_mode=EstimatorCalcMode.CRYSTAL_U0, model_version="v3.0.0")
calculator = ASECalculator(estimator)
pfp_api_client: 1.5.0
[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)
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)
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)
[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
*Force-consistent energies used in optimization.
FIRE: 0 06:54:54 -3603.041770* 1.1063
FIRE: 1 06:54:54 -3604.081779* 1.0498
FIRE: 2 06:54:54 -3605.848377* 0.9306
FIRE: 3 06:54:55 -3607.344865* 0.7998
FIRE: 4 06:54:55 -3608.622478* 0.6640
FIRE: 5 06:54:55 -3609.735569* 0.5327
FIRE: 6 06:54:55 -3610.728639* 0.4144
FIRE: 7 06:54:56 -3611.628229* 0.3549
FIRE: 8 06:54:56 -3612.447484* 0.3436
FIRE: 9 06:54:56 -3613.187570* 0.3175
FIRE: 10 06:54:56 -3613.846037* 0.2669
FIRE: 11 06:54:57 -3614.425194* 0.2127
FIRE: 12 06:54:57 -3614.931713* 0.2186
FIRE: 13 06:54:57 -3615.369616* 0.2122
FIRE: 14 06:54:57 -3615.738931* 0.1940
FIRE: 15 06:54:58 -3616.044471* 0.1671
FIRE: 16 06:54:58 -3616.293988* 0.1389
FIRE: 17 06:54:58 -3616.481608* 0.1185
FIRE: 18 06:54:58 -3616.616016* 0.1265
FIRE: 19 06:54:59 -3616.717579* 0.1232
FIRE: 20 06:54:59 -3616.798756* 0.1233
FIRE: 21 06:54:59 -3616.855684* 0.1492
FIRE: 22 06:54:59 -3616.885267* 0.1363
FIRE: 23 06:54:59 -3616.959217* 0.0793
FIRE: 24 06:55:00 -3617.036669* 0.0826
FIRE: 25 06:55:00 -3617.107673* 0.0584
FIRE: 26 06:55:00 -3617.151703* 0.0699
FIRE: 27 06:55:00 -3617.174603* 0.0587
FIRE: 28 06:55:01 -3617.184372* 0.0522
FIRE: 29 06:55:01 -3617.188934* 0.0450
FIRE: 30 06:55:01 -3617.196528* 0.0376
FIRE: 31 06:55:01 -3617.205299* 0.0348
FIRE: 32 06:55:02 -3617.213477* 0.0359
FIRE: 33 06:55:02 -3617.220633* 0.0334
FIRE: 34 06:55:02 -3617.227574* 0.0257
FIRE: 35 06:55:02 -3617.232732* 0.0232
FIRE: 36 06:55:03 -3617.237323* 0.0200
FIRE: 37 06:55:03 -3617.240054* 0.0153
FIRE: 38 06:55:03 -3617.241792* 0.0167
FIRE: 39 06:55:03 -3617.241965* 0.0160
FIRE: 40 06:55:04 -3617.242585* 0.0148
FIRE: 41 06:55:04 -3617.243465* 0.0137
FIRE: 42 06:55:04 -3617.244501* 0.0127
FIRE: 43 06:55:04 -3617.245454* 0.0120
FIRE: 44 06:55:04 -3617.246485* 0.0107
FIRE: 45 06:55:05 -3617.247410* 0.0099
FIRE: 46 06:55:05 -3617.248225* 0.0098
FIRE: 47 06:55:05 -3617.249551* 0.0087
FIRE: 48 06:55:05 -3617.250300* 0.0089
FIRE: 49 06:55:06 -3617.251227* 0.0085
FIRE: 50 06:55:06 -3617.252279* 0.0077
FIRE: 51 06:55:06 -3617.253040* 0.0069
FIRE: 52 06:55:06 -3617.254019* 0.0076
FIRE: 53 06:55:07 -3617.254870* 0.0066
FIRE: 54 06:55:07 -3617.256088* 0.0067
FIRE: 55 06:55:07 -3617.257146* 0.0056
FIRE: 56 06:55:07 -3617.257436* 0.0047
FIRE: 57 06:55:08 -3617.257554* 0.0054
FIRE: 58 06:55:08 -3617.257386* 0.0047
FIRE: 59 06:55:08 -3617.257621* 0.0035
FIRE: 60 06:55:08 -3617.257506* 0.0019
FIRE: 61 06:55:09 -3617.257658* 0.0023
FIRE: 62 06:55:09 -3617.257822* 0.0022
FIRE: 63 06:55:09 -3617.257604* 0.0020
FIRE: 64 06:55:09 -3617.257618* 0.0014
FIRE: 65 06:55:09 -3617.257748* 0.0024
FIRE: 66 06:55:10 -3617.257801* 0.0023
FIRE: 67 06:55:10 -3617.257863* 0.0020
FIRE: 68 06:55:10 -3617.257761* 0.0017
FIRE: 69 06:55:10 -3617.257774* 0.0013
FIRE: 70 06:55:11 -3617.257747* 0.0012
FIRE: 71 06:55:11 -3617.257610* 0.0012
FIRE: 72 06:55:11 -3617.257715* 0.0012
FIRE: 73 06:55:11 -3617.257872* 0.0011
FIRE: 74 06:55:12 -3617.257762* 0.0008
Optimizing Pd306Pt405
Step Time Energy fmax
*Force-consistent energies used in optimization.
FIRE: 0 06:55:12 -3128.362078* 0.5548
FIRE: 1 06:55:12 -3128.717762* 0.5195
FIRE: 2 06:55:12 -3129.326822* 0.4481
FIRE: 3 06:55:13 -3130.024355* 0.3421
FIRE: 4 06:55:13 -3130.656050* 0.2132
FIRE: 5 06:55:13 -3131.124641* 0.2397
FIRE: 6 06:55:13 -3131.515908* 0.3003
FIRE: 7 06:55:14 -3131.876732* 0.2811
FIRE: 8 06:55:14 -3132.204783* 0.1908
FIRE: 9 06:55:14 -3132.466579* 0.1373
FIRE: 10 06:55:14 -3132.646607* 0.1605
FIRE: 11 06:55:14 -3132.767194* 0.1392
FIRE: 12 06:55:15 -3132.856234* 0.1389
FIRE: 13 06:55:15 -3132.914484* 0.1162
FIRE: 14 06:55:15 -3132.932024* 0.1077
FIRE: 15 06:55:15 -3132.952750* 0.0965
FIRE: 16 06:55:16 -3132.987167* 0.0810
FIRE: 17 06:55:16 -3133.024548* 0.0684
FIRE: 18 06:55:16 -3133.056768* 0.0562
FIRE: 19 06:55:16 -3133.082869* 0.0605
FIRE: 20 06:55:17 -3133.105048* 0.0639
FIRE: 21 06:55:17 -3133.123677* 0.0667
FIRE: 22 06:55:17 -3133.140000* 0.0676
FIRE: 23 06:55:17 -3133.149982* 0.0533
FIRE: 24 06:55:18 -3133.153655* 0.0348
FIRE: 25 06:55:18 -3133.154709* 0.0330
FIRE: 26 06:55:18 -3133.157169* 0.0296
FIRE: 27 06:55:18 -3133.159644* 0.0249
FIRE: 28 06:55:19 -3133.162778* 0.0235
FIRE: 29 06:55:19 -3133.165806* 0.0222
FIRE: 30 06:55:19 -3133.168270* 0.0207
FIRE: 31 06:55:19 -3133.170877* 0.0216
FIRE: 32 06:55:19 -3133.173332* 0.0226
FIRE: 33 06:55:20 -3133.176405* 0.0225
FIRE: 34 06:55:20 -3133.179414* 0.0210
FIRE: 35 06:55:20 -3133.182049* 0.0183
FIRE: 36 06:55:20 -3133.184061* 0.0148
FIRE: 37 06:55:21 -3133.186380* 0.0139
FIRE: 38 06:55:21 -3133.188631* 0.0144
FIRE: 39 06:55:21 -3133.191543* 0.0132
FIRE: 40 06:55:21 -3133.194218* 0.0137
FIRE: 41 06:55:22 -3133.197142* 0.0146
FIRE: 42 06:55:22 -3133.199853* 0.0169
FIRE: 43 06:55:22 -3133.200693* 0.0123
FIRE: 44 06:55:22 -3133.200954* 0.0100
FIRE: 45 06:55:23 -3133.201204* 0.0091
FIRE: 46 06:55:23 -3133.201377* 0.0077
FIRE: 47 06:55:23 -3133.201237* 0.0061
FIRE: 48 06:55:23 -3133.201438* 0.0060
FIRE: 49 06:55:23 -3133.201492* 0.0059
FIRE: 50 06:55:24 -3133.201275* 0.0058
FIRE: 51 06:55:24 -3133.201387* 0.0056
FIRE: 52 06:55:24 -3133.201623* 0.0053
FIRE: 53 06:55:24 -3133.201515* 0.0049
FIRE: 54 06:55:25 -3133.201358* 0.0045
FIRE: 55 06:55:25 -3133.201637* 0.0039
FIRE: 56 06:55:25 -3133.201615* 0.0032
FIRE: 57 06:55:25 -3133.201658* 0.0026
FIRE: 58 06:55:26 -3133.201508* 0.0021
FIRE: 59 06:55:26 -3133.201398* 0.0012
FIRE: 60 06:55:26 -3133.201442* 0.0007
Optimizing Pd405Pt306
Step Time Energy fmax
*Force-consistent energies used in optimization.
FIRE: 0 06:55:26 -2921.182334* 0.8084
FIRE: 1 06:55:27 -2922.173634* 0.7782
FIRE: 2 06:55:27 -2923.798336* 0.7174
FIRE: 3 06:55:27 -2925.164742* 0.6494
FIRE: 4 06:55:27 -2926.294749* 0.5747
FIRE: 5 06:55:28 -2927.257778* 0.4948
FIRE: 6 06:55:28 -2928.103283* 0.4127
FIRE: 7 06:55:28 -2928.859668* 0.3310
FIRE: 8 06:55:28 -2929.541302* 0.2730
FIRE: 9 06:55:29 -2930.148359* 0.2152
FIRE: 10 06:55:29 -2930.679060* 0.1948
FIRE: 11 06:55:29 -2931.134719* 0.1854
FIRE: 12 06:55:29 -2931.522542* 0.1735
FIRE: 13 06:55:29 -2931.850052* 0.1563
FIRE: 14 06:55:30 -2932.122565* 0.1384
FIRE: 15 06:55:30 -2932.342232* 0.1254
FIRE: 16 06:55:30 -2932.512740* 0.1193
FIRE: 17 06:55:30 -2932.643065* 0.1234
FIRE: 18 06:55:31 -2932.741324* 0.1099
FIRE: 19 06:55:31 -2932.811902* 0.1033
FIRE: 20 06:55:31 -2932.859388* 0.1174
FIRE: 21 06:55:31 -2932.887646* 0.1096
FIRE: 22 06:55:32 -2932.943773* 0.0836
FIRE: 23 06:55:32 -2933.016130* 0.0667
FIRE: 24 06:55:32 -2933.083493* 0.0619
FIRE: 25 06:55:32 -2933.140449* 0.0486
FIRE: 26 06:55:33 -2933.176317* 0.0427
FIRE: 27 06:55:33 -2933.193285* 0.0424
FIRE: 28 06:55:33 -2933.196087* 0.0381
FIRE: 29 06:55:33 -2933.201024* 0.0305
FIRE: 30 06:55:34 -2933.206477* 0.0299
FIRE: 31 06:55:34 -2933.212568* 0.0299
FIRE: 32 06:55:34 -2933.218423* 0.0293
FIRE: 33 06:55:34 -2933.223804* 0.0279
FIRE: 34 06:55:34 -2933.228556* 0.0256
FIRE: 35 06:55:35 -2933.233788* 0.0222
FIRE: 36 06:55:35 -2933.238048* 0.0179
FIRE: 37 06:55:35 -2933.242471* 0.0179
FIRE: 38 06:55:35 -2933.246656* 0.0223
FIRE: 39 06:55:36 -2933.251570* 0.0203
FIRE: 40 06:55:36 -2933.257329* 0.0153
FIRE: 41 06:55:36 -2933.262312* 0.0190
FIRE: 42 06:55:36 -2933.265847* 0.0172
FIRE: 43 06:55:37 -2933.267247* 0.0097
FIRE: 44 06:55:37 -2933.267624* 0.0084
FIRE: 45 06:55:37 -2933.267822* 0.0065
FIRE: 46 06:55:37 -2933.268071* 0.0049
FIRE: 47 06:55:38 -2933.268362* 0.0047
FIRE: 48 06:55:38 -2933.268514* 0.0053
FIRE: 49 06:55:38 -2933.268724* 0.0051
FIRE: 50 06:55:38 -2933.268781* 0.0032
FIRE: 51 06:55:39 -2933.268824* 0.0026
FIRE: 52 06:55:39 -2933.268775* 0.0025
FIRE: 53 06:55:39 -2933.268761* 0.0024
FIRE: 54 06:55:39 -2933.268763* 0.0022
FIRE: 55 06:55:40 -2933.268797* 0.0020
FIRE: 56 06:55:40 -2933.268858* 0.0017
FIRE: 57 06:55:40 -2933.269053* 0.0016
FIRE: 58 06:55:40 -2933.268941* 0.0015
FIRE: 59 06:55:41 -2933.268795* 0.0014
FIRE: 60 06:55:41 -2933.269019* 0.0012
FIRE: 61 06:55:41 -2933.268959* 0.0009
Optimizing Pd711
Step Time Energy fmax
*Force-consistent energies used in optimization.
FIRE: 0 06:55:41 -2415.404839* 0.3443
FIRE: 1 06:55:42 -2415.612567* 0.3219
FIRE: 2 06:55:42 -2415.978111* 0.2807
FIRE: 3 06:55:42 -2416.425075* 0.2268
FIRE: 4 06:55:43 -2416.882951* 0.1757
FIRE: 5 06:55:43 -2417.313176* 0.1856
FIRE: 6 06:55:43 -2417.704316* 0.1983
FIRE: 7 06:55:43 -2418.042082* 0.1825
FIRE: 8 06:55:44 -2418.336027* 0.1449
FIRE: 9 06:55:44 -2418.583665* 0.1194
FIRE: 10 06:55:44 -2418.783262* 0.1272
FIRE: 11 06:55:44 -2418.940327* 0.1277
FIRE: 12 06:55:45 -2419.064507* 0.1063
FIRE: 13 06:55:45 -2419.160729* 0.0951
FIRE: 14 06:55:45 -2419.227246* 0.0895
FIRE: 15 06:55:45 -2419.261509* 0.0613
FIRE: 16 06:55:46 -2419.268033* 0.0809
FIRE: 17 06:55:46 -2419.278819* 0.0741
FIRE: 18 06:55:46 -2419.296931* 0.0616
FIRE: 19 06:55:46 -2419.317336* 0.0530
FIRE: 20 06:55:47 -2419.336185* 0.0464
FIRE: 21 06:55:47 -2419.352537* 0.0396
FIRE: 22 06:55:47 -2419.367761* 0.0400
FIRE: 23 06:55:47 -2419.381849* 0.0326
FIRE: 24 06:55:48 -2419.394014* 0.0228
FIRE: 25 06:55:48 -2419.401561* 0.0276
FIRE: 26 06:55:48 -2419.405173* 0.0324
FIRE: 27 06:55:48 -2419.405838* 0.0308
FIRE: 28 06:55:49 -2419.406837* 0.0277
FIRE: 29 06:55:49 -2419.408552* 0.0233
FIRE: 30 06:55:49 -2419.410071* 0.0179
FIRE: 31 06:55:49 -2419.411548* 0.0118
FIRE: 32 06:55:50 -2419.412595* 0.0128
FIRE: 33 06:55:50 -2419.413697* 0.0138
FIRE: 34 06:55:50 -2419.414823* 0.0132
FIRE: 35 06:55:50 -2419.416163* 0.0107
FIRE: 36 06:55:51 -2419.417414* 0.0096
FIRE: 37 06:55:51 -2419.418938* 0.0088
FIRE: 38 06:55:51 -2419.419777* 0.0118
FIRE: 39 06:55:51 -2419.420586* 0.0149
FIRE: 40 06:55:52 -2419.421830* 0.0146
FIRE: 41 06:55:52 -2419.423231* 0.0102
FIRE: 42 06:55:52 -2419.424453* 0.0101
FIRE: 43 06:55:52 -2419.425412* 0.0134
FIRE: 44 06:55:53 -2419.426300* 0.0084
FIRE: 45 06:55:53 -2419.426488* 0.0067
FIRE: 46 06:55:53 -2419.426516* 0.0058
FIRE: 47 06:55:53 -2419.426643* 0.0042
FIRE: 48 06:55:54 -2419.426744* 0.0028
FIRE: 49 06:55:54 -2419.426760* 0.0038
FIRE: 50 06:55:54 -2419.426823* 0.0041
FIRE: 51 06:55:54 -2419.426850* 0.0032
FIRE: 52 06:55:55 -2419.426919* 0.0028
FIRE: 53 06:55:55 -2419.426806* 0.0020
FIRE: 54 06:55:55 -2419.426866* 0.0020
FIRE: 55 06:55:55 -2419.426900* 0.0018
FIRE: 56 06:55:56 -2419.426932* 0.0016
FIRE: 57 06:55:56 -2419.426878* 0.0014
FIRE: 58 06:55:56 -2419.426941* 0.0013
FIRE: 59 06:55:56 -2419.426897* 0.0011
FIRE: 60 06:55:57 -2419.426934* 0.0010
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 = -44.26 meV
Excess energy of Pd405Pt306 = 2.36 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 since its excess energy is positive.
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 [196 552 99 568 368 382 471 105 599 212 637 142 432 304 663 49 680 302
493 104 232 102 487 433 273 420 314 185 61 435 132 576 561 374 350 85
581 240 13 699 666 359 616 571 600 110 327 201 8 347 146 55 593 351
391 157 658 244 463 236 288 691 166 90 118 528 72 686 562 591 437 135
690 4 702 225 137 223 404 138 98 145 623 676 525 621 64 466 328 221
330 626 281 529 208 269 548 647 150 527 377 313 672 206 507 5 203 256
584 375 317 614 100 602 510 217 394 315 649 414 312 661 27 467 673 540
704 425 358 551 239 385 250 28 205 122 373 264 413 565 267 286 343 456
601 230 386 532 307 153 556 679 172 91 655 569 202 268 181 95 484 173
707 19 514 509 277 537 638 11 311 390 700 33 458 405 555 29 511 168
684 363 428 590 444 371 303 65 594 366 361 450 566 657 520 550 338 154
246 18 334 464 336 275 20 633 176 160 620 697 558 80 83 195 335 325
305 0 278 117 597 615 131 671 322 674 128 438 596 133 254 197 439 47
23 140 191 296 403 73 82 107 66 37 474 7 226 6 360 187 651 234
344 418 3 249 213 96 227 557 39 31 628 417 136 346 475 42 534 504
441 364 52 245 2 50 46 426 209 498 688 480 40 43 632 272 258 93
397 194 606 144 34 560 353 559 126 253 283 642 321 276 291 67 648 580
627 329 694 58 1 170 478 207 705 88 370 395 549 573 592 396 139 629
675 610 481 123 618 219 411 120 667 224 310 400 423 640 103 526 654 348
308 409 407 119 81 54 365 469 656 84 659 644 677 536 164 452 78 612
115 200 639 546 297 214 515 635 326 76 379 290 483 678 564 554 553 339
499 51 369 429 220 392 681 162 151 174 218 443 542 210 270 698 177 419
399 624 708 582 706 355 563 545 257]
[12]:
print("Optimizing Pd405Pt306_random")
Pd405Pt306_random.calc = calculator
E_pd405pt306_random = get_opt_energy(Pd405Pt306_random)
Optimizing Pd405Pt306_random
Step Time Energy fmax
*Force-consistent energies used in optimization.
FIRE: 0 06:55:57 -2951.634114* 0.7943
FIRE: 1 06:55:58 -2952.049965* 0.7585
FIRE: 2 06:55:58 -2952.770701* 0.6876
FIRE: 3 06:55:58 -2953.619475* 0.5777
FIRE: 4 06:55:58 -2954.359894* 0.4618
FIRE: 5 06:55:58 -2954.930649* 0.3488
FIRE: 6 06:55:59 -2955.380034* 0.3323
FIRE: 7 06:55:59 -2955.741782* 0.2891
FIRE: 8 06:55:59 -2956.033248* 0.2633
FIRE: 9 06:55:59 -2956.257166* 0.2117
FIRE: 10 06:56:00 -2956.416871* 0.2094
FIRE: 11 06:56:00 -2956.526379* 0.1835
FIRE: 12 06:56:00 -2956.604745* 0.1840
FIRE: 13 06:56:00 -2956.665961* 0.1816
FIRE: 14 06:56:01 -2956.716348* 0.1827
FIRE: 15 06:56:01 -2956.747297* 0.1770
FIRE: 16 06:56:01 -2956.800838* 0.1661
FIRE: 17 06:56:01 -2956.863802* 0.1508
FIRE: 18 06:56:02 -2956.923657* 0.1316
FIRE: 19 06:56:02 -2956.973257* 0.1091
FIRE: 20 06:56:02 -2957.010412* 0.0848
FIRE: 21 06:56:02 -2957.036208* 0.0725
FIRE: 22 06:56:03 -2957.052796* 0.0641
FIRE: 23 06:56:03 -2957.059193* 0.0881
FIRE: 24 06:56:03 -2957.060665* 0.0824
FIRE: 25 06:56:03 -2957.063410* 0.0714
FIRE: 26 06:56:04 -2957.067207* 0.0563
FIRE: 27 06:56:04 -2957.071634* 0.0525
FIRE: 28 06:56:04 -2957.076364* 0.0490
FIRE: 29 06:56:05 -2957.081169* 0.0447
FIRE: 30 06:56:05 -2957.085771* 0.0398
FIRE: 31 06:56:05 -2957.090457* 0.0345
FIRE: 32 06:56:05 -2957.095123* 0.0304
FIRE: 33 06:56:06 -2957.099647* 0.0258
FIRE: 34 06:56:06 -2957.103869* 0.0232
FIRE: 35 06:56:06 -2957.107772* 0.0231
FIRE: 36 06:56:06 -2957.111816* 0.0323
FIRE: 37 06:56:07 -2957.116451* 0.0284
FIRE: 38 06:56:07 -2957.121823* 0.0296
FIRE: 39 06:56:07 -2957.127640* 0.0272
FIRE: 40 06:56:07 -2957.133752* 0.0266
FIRE: 41 06:56:08 -2957.139396* 0.0144
FIRE: 42 06:56:08 -2957.142666* 0.0255
FIRE: 43 06:56:08 -2957.143234* 0.0215
FIRE: 44 06:56:08 -2957.143503* 0.0199
FIRE: 45 06:56:09 -2957.144038* 0.0169
FIRE: 46 06:56:09 -2957.144598* 0.0126
FIRE: 47 06:56:09 -2957.145193* 0.0086
FIRE: 48 06:56:09 -2957.145683* 0.0064
FIRE: 49 06:56:10 -2957.146011* 0.0062
FIRE: 50 06:56:10 -2957.146141* 0.0072
FIRE: 51 06:56:10 -2957.146298* 0.0100
FIRE: 52 06:56:10 -2957.146495* 0.0109
FIRE: 53 06:56:11 -2957.146689* 0.0105
FIRE: 54 06:56:11 -2957.147045* 0.0092
FIRE: 55 06:56:11 -2957.147453* 0.0061
FIRE: 56 06:56:11 -2957.147860* 0.0046
FIRE: 57 06:56:12 -2957.148160* 0.0034
FIRE: 58 06:56:12 -2957.148237* 0.0061
FIRE: 59 06:56:12 -2957.148304* 0.0058
FIRE: 60 06:56:12 -2957.148361* 0.0053
FIRE: 61 06:56:13 -2957.148444* 0.0045
FIRE: 62 06:56:13 -2957.148528* 0.0035
FIRE: 63 06:56:13 -2957.148574* 0.0030
FIRE: 64 06:56:13 -2957.148677* 0.0025
FIRE: 65 06:56:14 -2957.148703* 0.0025
FIRE: 66 06:56:14 -2957.148775* 0.0028
FIRE: 67 06:56:14 -2957.148754* 0.0034
FIRE: 68 06:56:14 -2957.148923* 0.0032
FIRE: 69 06:56:15 -2957.149008* 0.0028
FIRE: 70 06:56:15 -2957.149121* 0.0022
FIRE: 71 06:56:15 -2957.149235* 0.0016
FIRE: 72 06:56:15 -2957.149309* 0.0021
FIRE: 73 06:56:16 -2957.149395* 0.0027
FIRE: 74 06:56:16 -2957.149500* 0.0020
FIRE: 75 06:56:16 -2957.149619* 0.0016
FIRE: 76 06:56:16 -2957.149768* 0.0020
FIRE: 77 06:56:17 -2957.149799* 0.0027
FIRE: 78 06:56:17 -2957.149842* 0.0049
FIRE: 79 06:56:17 -2957.149897* 0.0014
FIRE: 80 06:56:17 -2957.149829* 0.0028
FIRE: 81 06:56:18 -2957.149892* 0.0023
FIRE: 82 06:56:18 -2957.149865* 0.0013
FIRE: 83 06:56:18 -2957.149865* 0.0005
[13]:
view_ngl(Pd405Pt306_random)
[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 = -31.22 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"])
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"])
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)
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"])
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"])
[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.CRYSTAL, model_version="v3.0.0")
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: 1.5.0
Step Time Energy fmax
*Force-consistent energies used in optimization.
FIRE: 0 06:58:31 -1860.090772* 2.7723
FIRE: 1 06:58:31 -1866.458047* 2.3451
FIRE: 2 06:58:31 -1871.904323* 2.0879
FIRE: 3 06:58:31 -1876.434307* 2.0256
FIRE: 4 06:58:32 -1880.091439* 1.9501
FIRE: 5 06:58:32 -1882.952912* 1.8591
FIRE: 6 06:58:32 -1885.147381* 1.7505
FIRE: 7 06:58:32 -1886.867019* 1.6223
FIRE: 8 06:58:32 -1888.358989* 1.4732
FIRE: 9 06:58:33 -1889.852164* 1.4049
FIRE: 10 06:58:33 -1891.473457* 1.2978
FIRE: 11 06:58:33 -1893.201623* 1.0758
FIRE: 12 06:58:33 -1894.904770* 0.9423
FIRE: 13 06:58:33 -1896.433910* 0.9369
FIRE: 14 06:58:33 -1897.707551* 0.9101
FIRE: 15 06:58:34 -1898.742282* 0.8622
FIRE: 16 06:58:34 -1899.634513* 0.8619
FIRE: 17 06:58:34 -1900.494577* 0.9636
FIRE: 18 06:58:34 -1901.380985* 1.0611
FIRE: 19 06:58:34 -1902.273167* 1.1440
FIRE: 20 06:58:35 -1903.098770* 1.2041
FIRE: 21 06:58:35 -1903.779610* 1.2391
FIRE: 22 06:58:35 -1904.287751* 1.2520
FIRE: 23 06:58:35 -1904.671516* 1.1932
FIRE: 24 06:58:35 -1905.006171* 0.9333
FIRE: 25 06:58:35 -1905.331511* 0.7080
FIRE: 26 06:58:36 -1905.631789* 0.3967
FIRE: 27 06:58:36 -1905.853587* 0.3487
FIRE: 28 06:58:36 -1905.981356* 0.5745
FIRE: 29 06:58:36 -1906.069182* 0.9726
FIRE: 30 06:58:36 -1906.184962* 1.1589
FIRE: 31 06:58:37 -1906.327430* 1.0321
FIRE: 32 06:58:37 -1906.441560* 0.5956
FIRE: 33 06:58:37 -1906.530019* 0.5836
FIRE: 34 06:58:37 -1906.645967* 0.6519
FIRE: 35 06:58:37 -1906.778954* 0.5218
FIRE: 36 06:58:38 -1906.857004* 0.5165
FIRE: 37 06:58:38 -1906.938558* 0.6041
FIRE: 38 06:58:38 -1906.935862* 0.4992
FIRE: 39 06:58:38 -1907.073519* 0.2194
FIRE: 40 06:58:38 -1907.089033* 0.2654
FIRE: 41 06:58:38 -1907.099305* 0.2227
FIRE: 42 06:58:39 -1907.114434* 0.1484
FIRE: 43 06:58:39 -1907.127182* 0.0941
FIRE: 44 06:58:39 -1907.133570* 0.1261
FIRE: 45 06:58:39 -1907.136339* 0.1818
FIRE: 46 06:58:39 -1907.141304* 0.1904
FIRE: 47 06:58:40 -1907.151191* 0.1533
FIRE: 48 06:58:40 -1907.166380* 0.0895
FIRE: 49 06:58:40 -1907.182247* 0.0821
FIRE: 50 06:58:40 -1907.193445* 0.1250
FIRE: 51 06:58:40 -1907.202915* 0.1232
FIRE: 52 06:58:41 -1907.216335* 0.0986
FIRE: 53 06:58:41 -1907.231155* 0.1026
FIRE: 54 06:58:41 -1907.241449* 0.0983
FIRE: 55 06:58:41 -1907.250398* 0.0815
FIRE: 56 06:58:41 -1907.262611* 0.1171
FIRE: 57 06:58:41 -1907.273228* 0.0856
FIRE: 58 06:58:42 -1907.286393* 0.1087
FIRE: 59 06:58:42 -1907.303588* 0.0944
FIRE: 60 06:58:42 -1907.324283* 0.0848
FIRE: 61 06:58:42 -1907.341892* 0.1294
FIRE: 62 06:58:42 -1907.366470* 0.2103
FIRE: 63 06:58:43 -1907.376558* 0.0905
FIRE: 64 06:58:43 -1907.376744* 0.1445
FIRE: 65 06:58:43 -1907.378749* 0.1131
FIRE: 66 06:58:43 -1907.381442* 0.0907
FIRE: 67 06:58:43 -1907.383602* 0.0909
FIRE: 68 06:58:43 -1907.384749* 0.0914
FIRE: 69 06:58:44 -1907.385938* 0.1034
FIRE: 70 06:58:44 -1907.388170* 0.1048
FIRE: 71 06:58:44 -1907.391782* 0.0969
FIRE: 72 06:58:44 -1907.396161* 0.0992
FIRE: 73 06:58:44 -1907.400149* 0.1017
FIRE: 74 06:58:45 -1907.404630* 0.1045
FIRE: 75 06:58:45 -1907.411236* 0.1076
FIRE: 76 06:58:45 -1907.419713* 0.1128
FIRE: 77 06:58:45 -1907.429156* 0.1202
FIRE: 78 06:58:45 -1907.442226* 0.1303
FIRE: 79 06:58:45 -1907.459426* 0.1469
FIRE: 80 06:58:46 -1907.482334* 0.1695
FIRE: 81 06:58:46 -1907.513214* 0.1997
FIRE: 82 06:58:46 -1907.553925* 0.2049
FIRE: 83 06:58:46 -1907.606483* 0.2176
FIRE: 84 06:58:46 -1907.672910* 0.2368
FIRE: 85 06:58:47 -1907.736053* 0.1768
FIRE: 86 06:58:47 -1907.758212* 0.3063
FIRE: 87 06:58:47 -1907.774582* 0.2071
FIRE: 88 06:58:47 -1907.775030* 0.2446
FIRE: 89 06:58:47 -1907.778554* 0.1891
FIRE: 90 06:58:48 -1907.783050* 0.1214
FIRE: 91 06:58:48 -1907.785487* 0.1070
FIRE: 92 06:58:48 -1907.785702* 0.1232
FIRE: 93 06:58:48 -1907.785959* 0.1161
FIRE: 94 06:58:48 -1907.786526* 0.1023
FIRE: 95 06:58:49 -1907.787278* 0.0949
FIRE: 96 06:58:49 -1907.788106* 0.0931
FIRE: 97 06:58:49 -1907.788830* 0.0909
FIRE: 98 06:58:49 -1907.789506* 0.0884
FIRE: 99 06:58:49 -1907.790147* 0.0854
FIRE: 100 06:58:50 -1907.790779* 0.0819
FIRE: 101 06:58:50 -1907.791550* 0.0778
FIRE: 102 06:58:50 -1907.792600* 0.0732
FIRE: 103 06:58:50 -1907.794079* 0.0685
FIRE: 104 06:58:50 -1907.795912* 0.0695
FIRE: 105 06:58:51 -1907.797794* 0.0704
FIRE: 106 06:58:51 -1907.799814* 0.0711
FIRE: 107 06:58:51 -1907.802043* 0.0714
FIRE: 108 06:58:51 -1907.804774* 0.0714
FIRE: 109 06:58:51 -1907.808127* 0.0711
FIRE: 110 06:58:52 -1907.811485* 0.0726
FIRE: 111 06:58:52 -1907.815417* 0.0736
FIRE: 112 06:58:52 -1907.820169* 0.0734
FIRE: 113 06:58:52 -1907.825160* 0.0712
FIRE: 114 06:58:52 -1907.831222* 0.0711
FIRE: 115 06:58:53 -1907.837461* 0.0696
FIRE: 116 06:58:53 -1907.844796* 0.0708
FIRE: 117 06:58:53 -1907.852221* 0.0708
FIRE: 118 06:58:53 -1907.859615* 0.0690
FIRE: 119 06:58:53 -1907.867319* 0.0682
FIRE: 120 06:58:54 -1907.875094* 0.1026
FIRE: 121 06:58:54 -1907.875724* 0.2086
FIRE: 122 06:58:54 -1907.883200* 0.0815
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[25]:
SnO2_Pt119 = Trajectory("./SnO2_Pt119.traj")
view_ngl(SnO2_Pt119, representations=["ball+stick"])
[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
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