Title Page 2

ABSTRACT 5

Contents 9

TECHNICAL TERMS AND ABBREVIATIONS 24

Chapter 1. INTRODUCTION 26

1.1. Surface and its important applications 26

1.2. Modelling and simulation of surface 28

1.3. Challenging for modelling surface and interface 31

Chapter 2. LITERATURE REVIEW 35

2.1. MLFF for searching stable surface 35

2.2. MLFF accelerating catalyst surface exploration 36

2.3. MLFF for surface reconstruction 38

2.4. MLFF for complex kinetic process on surface/interface 41

Chapter 3. METHODOLOGIES 45

3.1. Introduction 45

3.2. First principle calculation 46

3.2.1. Born-Oppenheimer approximation 47

3.2.2. Hartree-Fock method 47

3.2.3. Density functional theory 49

3.2.4. Exchange-correlation functional and dispersion correction 51

3.2.5. Ab initio molecular dynamics 52

3.2.6. VASP package 53

3.3. Molecular dynamics 53

3.3.1. Newtonian mechanics 54

3.3.2. Molecular dynamics workflow 54

3.3.3. Verlet algorithm 56

3.3.4. Statistical ensemble 56

3.3.5. Periodic boundary conditions 57

3.3.6. Cutoff 58

3.3.7. LAMMPS package 58

3.4. Empirical potential 59

3.4.1. Two-body potential 59

3.4.2. Many-body potential 60

3.4.3. Molecular force field 61

3.5. Machine learning force field 61

3.5.1. Kemal-based Method 62

3.5.2. Artificial neural network 62

3.5.3. Example of MLFF model 63

3.5.4. Data collection and preparation 64

Chapter 4. COMPREHENSIVE ASSESSMENT OF CLASSICAL FORCE FIELD FOR CARBON MATERIALS 67

4.1. Introduction 67

4.2. Lattice constant for crystalline phase carbon 70

4.3. Cohesive energy and formation energy 71

4.4. Structure and formation energy of graphene defect 72

4.4.1. Single vacancy defect in graphene lattice 73

4.4.2. Double vacancy defect in graphene lattice 75

4.4.3. Stone-Wales defect in graphene lattice 77

4.4.4. Ad atoms defect in graphene lattice 78

4.5. Graphene edge energy 81

4.6. Interlayer interaction in bilayer graphene 82

4.7. Thermal stability of C₆₀ 86

4.8. Mechanical properties of graphene and CNT 88

4.8.1. Single crystalline graphene uniaxial tensile test 90

4.8.2. Carbon nanotube uniaxial tensile test 93

4.9. Conclusion 96

Chapter 5. HIGHT-TEMPERATURE HIGH-PRESSURE DIAMOND GROWTH MECHANISM 99

5.1. Introduction 99

5.2. Preparing the training set 105

5.2.1. Initial training set 105

5.2.2. Training set expropriation 106

5.3. Diamond growth in iron carbides 109

5.3.1. Diamond nucleation in iron carbides 109

5.3.2. Morphology of the HTHP diamond 111

5.4. Growth kinetics of diamond surfaces 114

5.4.1. MD setting for diamond surfaces growth 114

5.4.2. Growth kinetics of (100) surface 115

5.4.3. Growth kinetics of (110) surface 117

5.4.4. Growth kinetics of (111) surface 119

5.5. 2D nucleation on (111) surface 121

5.6. Conclusion 127

Chapter 6. THE RECONSTRUCTION OF PT(004) SURFACE AND THE VICINAL PT(001) SURFACES 129

6.1. Introduction 129

6.2. Training set preparation 134

6.3. NNP training and validation 135

6.4. Driving force of the quasi-hexagonal reconstruction 140

6.5. Pristine Pt(001) to Pt(001) quasi-hexagonal reconstruction 145

6.6. Surface deposition and step induced reconstruction 148

6.7. The reconstruction of vicinal Pt(001) high-index surfaces 152

6.8. Conclusion 154

Chapter 7. CONCLUSION AND PERSPECTIVE 156

REFERENCES 159

Table 1.1. The energy and force error for molecules in MD-17 data set, predicted by various MLFF... 33

Table 4.1. The lattice constant of the crystalline carbon predicted by the empirical bond order potential,... 71

Table 4.2. Defect formation energy and geometry information of SV in graphene, predicted by empirical... 75

Table 4.3. The formation energy and atomic structure of DV, predicted by DFT and potentials 76

Table 4.4. Defect formation energy and geometry information of SW defect in graphene, predicted by... 78

Table 4.5. Formation energy and atomic distances around the single ad-atom defect, represent top site 79

Table 4.6. The structure information (atomic distances and angle) around the add dimmer defect and the... 81

Table 4.7. The edge energies of graphene and CNTs predicted by CBOPs, GAP-20, and DFT 82

Table 4.8. The theoretical strength of the single crystalline, bi-crystalline, and polycrystalline... 89

Table 4.9. The mechanical properties of graphene along armchair (AC) and zigzag (ZZ) direction,... 93

Table 4.10. The mechanical properties of CNT (5,5) and CNT (10,0), including graphene failure strain,... 96

Table 5.1. NEP training parameters in nep.in (the input file for NEP training.) 108

Table 5.2. The edge energy of ZiaZag edge and Armchair edge of (111) surface 123

Table 5.3. The edge energy of different edge direction in (100) and (110) surface 125

Table 6.1. The mechanical properties of FCC Pt crystal calculated using different method. All results... 138

Table 6.2. The formation energies of some pristine Pt surfaces calculated by DFT, NNP and MEAM,... 140

Table 6.3. The surface stress of pristine Pt(001), (5×1), (5×N), (6×N), (7×N) surface alone the [110] and... 142

 Wolfgang Pauli once stated that 'God created the bulk, the surface was invented by the devil'. This quotation emphasizes the complexity and difficulty of studying material surfaces. For over a century, researchers have been fascinated by the properties of surface structures. Atoms on the surfaces and interfaces of materials experience a markedly different environment than bulk atoms. Surface atoms are bound to the bulk atom on one side and exposed or in contact with other substances on the other. Due to the sudden termination of the lattice at the surface, the outermost atoms at the surface form dangling bonds and the high surface energy. In order to eliminate dangling bonds and to reduce surface energy, there is reconstruction or surface passivation. Reconstruction and surface passivation affect many properties of materials such as catalysis, electrical conductivity, thermal conductivity, mechanics, etc., as well as kinetic processes occurring at the surface interface, such as growth, fracture, catalytic processes, etc. This is why it is important to understand the precise atomic structure of the surface interface of a material. Several experimental methods are available to characterize the surface structure, such as LEED, STM, TEM, and AFM. However, characterizing the surface structure under real conditions remains challenging. The dynamic evolution of surface and interfacial structures during catalysis requires in situ characterization to fully comprehend the atomic-scale synthesis and catalytic mechanism of the material.

In addition to experimental characterization, theoretical modelling allows us to understand the effect of surfaces on the thermodynamic and kinetic behaviour of materials at the atomic scale. There are two commonly used simulation methods: density-functional theory (DFT) and molecular dynamics simulation (MD). DFT is very accurate but computationally complex, making it difficult to apply to systems with more than 1,000 atoms. MD is known for its excellent computational efficiency and can simulate the dynamics of hundreds of millions of atoms on nanosecond time scales. However, MD simplifies the interatomic interactions, resulting in less accurate simulations. As a result, traditional modelling methods are still difficult to accurately simulate large-scale surface systems.

With the rapid development of machine learning (ML) methods, the machine learning force field (MLFF) has been introduced in theoretical modelling. Due to their powerful fitting capabilities, MLFFs can learn the interatomic interactions from ab initio calculations for application in MD simulations with high accuracy. Moreover, the computational complexity of MLFF is (O(N)), and hundreds of millions of atoms can be simulated with high computational efficiency. In this thesis, MLFF is introduced to simulate the growth of diamond under high temperature and high pressure (HTHP) conditions, and the reconstruction of Pt(001) quasi hexagonal surface.

In Chapter 1, we provide an overview of the traditional theoretical modelling approaches to studying surface structure and properties, as well as the limitations inherent in these approaches. Additionally, we have outlined the advantages of MLFF. Chapter 2 introduces the application of MLFF to surface and interface studies, illustrating the advantages of MLFF in terms of accuracy and computational efficiency. Chapter 3 introduces the methods used in this thesis, including DFT, MD and MLFF.

Chapter 4 provides a comprehensive comparison of commonly used force fields (empirical and MLFF fields) for carbon materials (graphene, graphite, diamond, carbon nanotube, and C₆₀). The results demonstrate that the MLFF well described the lattice constants, defect properties, and thermal stability of carbon materials. Additionally, the MLFF can simulate the fracture process and interface for graphene and carbon nanotubes, which is not possible with the empirical force field, unless modify the cutoff. However, the MLFF has limitations in describing the weak interactions such as van der Waals, which require further attention.

In Chapter 5, a Fe-C binary MLFF with ab initio accuracy was constructed to investigate the growth mechanism of HTHP diamond. Initially, MD simulations were conducted to analyse the diamond nucleation free energy, in conjunction with classical nucleation theory. This revealed a high nucleation barrier that impedes diamond nucleation. Subsequently, MD simulations were performed to grow a cuboctahedra diamond particle, and its morphology aligned well with the experimental observations. In order to gain insight into the morphological differences between HTHP diamond and natural diamond, the growth kinetics of several low-index diamond surfaces were examined. The findings indicate that the (111) surface exhibits a nucleation process, while the (100) and (110) surfaces undergo multilayer simultaneous growth processes.

Chapter 6 introduces the thermodynamic and kinetic properties of Pt(001) quasi-hexagonal surface reconstruction, using the adaptive learning MLFFs. The findings indicate that the surface energy, coordination number, and surface stress work together to drive the quasi-hexagonal reconstruction of Pt(001) rather than merely surface stress relaxation alone. Furthermore, large-scale molecular dynamics simulations demonstrated that the surface reconstruction of pristine Pt(001) leads to the formation of vacant surface area on the surface. The exposed subsurface is reconstructed as a hexagonal lattice, while the structure underneath the covered surface remains a square lattice, consistent with previous experimental research. Moreover, the deposition of Pt atoms and the formation of steps-induced surface reconstruction were studied. It has been demonstrated that surface reconstruction can occur in the presence of steps at 500 K. Furthermore, the post-annealing morphology of the vicinal Pt(001) surface was investigated, where the surface loses its sharp steps and becomes a shell-like structure.