Title Page
Abstract
Contents
Chapter 1. Introduction 22
1.1. Motivation 22
1.2. Brief review on perovskite- and antiperovskite-based batteries 24
1.3. The potential of antiperovskite electrolytes: a pathway towards high-performance SSE 26
1.4. The glassy state of matter 31
1.5. Experiment and modelling state of art of Li₃OCl and Na₃OCl as electrolye material 32
1.6. Project ambition, positioning and objectives 33
Chapter 2. Computational Methods and Models 36
2.1. Lattice dynamics, Gibbs free energy 36
2.1.1. Harmonic approximation 36
2.1.2. Pertubative and nonpertubative approximation 37
2.2. Density functional theory 44
2.2.1. Schrödinger equation 46
2.2.2. Born-Oppenheimer approximation 47
2.2.3. Independent electron approximation 47
2.2.4. Thomas-Fermi-Dirac approximation 49
2.2.5. Hohenberg-Kohn theorems 49
2.2.6. The Kohn-Sham Equation 50
2.2.7. The Exchange-Correlation Term 52
2.2.8. Pseudopotential method 53
2.2.9. Plane wave basis set 54
2.2.10. Total energy 55
2.3. Molecular dynamics 56
2.3.1. First principles molecular dynamics 56
2.3.2. Classical MD 58
2.4. Machine learning interatomic potentials 59
2.4.1. General overview 59
2.4.2. Gaussian Approximation Potential methodology 61
Chapter 3. Structural stability and ionic transport of crystalline antiperovskite Na₃OCl 64
3.1. Introduction 64
3.2. Computational methods 67
3.2.1. Harmonic phonon calculations 67
3.2.2. Quasi-harmonic approximation 68
3.2.3. Self-consistent phonon approach 69
3.3. Result and discussion 71
3.3.1. Structural stability 71
3.3.2. Electronic structure and ionic transport properties 85
3.4. Summary 86
Chapter 4. Unveiling the structure and ions dynamics of amorphous Na₃₋ₓOHₓCl antiperovskite electrolytes 88
4.1. Motivation 88
4.2. Calculation methodology and models 90
4.2.1. Producing Na₃₋ₓOHₓCl amorphous models at 300 K 90
4.2.2. Dynamical simulations at finite temperatures 91
4.3. Result and discussion 95
4.3.1. Structural properties 95
4.3.2. Dynamical properties 105
4.4. Summary 114
Chapter 5. First quantitative assessment of the structure of amorphous antiperovskite Na₃OCl by first-principles and machine learning molecular dynamics 116
5.1. Introduction 116
5.2. Computational methodology and models 118
5.2.1. First-principles molecular dynamic simulations 118
5.2.2. DFT-FPMD database composition 119
5.2.3. MLP-GAP molecular dynamics simulations 119
5.3. Results and discussion 119
5.3.1. Machine learning interatomic potential: model fitting and training database 119
5.3.2. MLP-GAP model performance assessment: errors for testing versus training set 120
5.3.3. Total X-rays and Neutrons structure factors 123
5.3.4. Total and partial pair correlation functions 124
Chapter 6. General conclusions and future perspectives 130
6.1. Conclusions 130
6.2. Future perspectives 132
References 134
List of publications 159
Table 3.1. Cubic-to-orthorhombic phase transition temperatures are calculated by the QP theory at different levels. Two values in each cell show the transition temperatures estimated... 84
Table 4.1. Upper part: nearest-neighbour interatomic distances rij (in Å) identified by the position of the first maximum of the pair correlation functions gij(r). We also give the...[이미지참조] 97
Table 4.2. Distribution of the individual cation-anion nα(l) structural units where an atom of species α (Na, Cl or O) is l-fold coordinated to a counter ion computed for glassy Na₃OCl...[이미지참조] 103
Table 4.3. Na tracer diffusion coefficients (D*), Na ions tracer (σ*), charge (σσ) and total conductivities (σtot), activation energies (Ea) and Haven ratio (HRJ,tot) extrapolated at T=300...[이미지참조] 113
Table 5.1. Hyperparameters of the GAP Model. Note that modified values for energy, force and virial are used for a number of sets of configurations. 121
Table 5.2. Bond lengths rij (in) in terms of position of the first maximum of the pair correlation functions gij (r) and average coordination number n obtained by FPMD and MLP models GAP1 and GAP3, respectively. For completeness, we also report the...[이미지참조] 126
Table 5.3. Distribution of the individual cation-anion nα(l) structural units where an atom of species α (Na, Cl or O) is l-fold coordinated to a counter ion computed for glassy Na₃OCl....[이미지참조] 127
Figure 2.1. Schematic representation of the temperature dependence of the square of the frequency of a soft mode. Below the temperature Tc the frequency is imaginary and hence...[이미지참조] 43
Figure 2.2. Machine-learning-based interatomic potentials methodology. Top: General overview and main required com- ponents. Bottom: Three main classes of regression methods... 59
Figure 2.3. Comparative flowchart of total energy calculations with traditional interatomic potentials (left) and ML interatomic potentials (right) 60
Figure 3.1. (a) Phonon band structure and (b) density of states of the cubic Pm ¯3m phase. The soft modes at M and R points in the phonon band structure indicate that the cubic Pm ¯3m phase...[이미지참조] 73
Figure 3.2. (a) Nontilted cubic Pm ¯3m crystal structure is denoted by a⁰a⁰a⁰. (b) M₃⁺ distortion indicates in-phase rotation (the same rotation direction of octahedral layers along an axis)[이미지참조] 75
Figure 3.3. (a) Phonon dispersion curves and (b) total and partial densities of states of monoclinic P2₁/m. The phonon dispersion curves and the total density of states show no... 76
Figure 3.4. Temperature-dependent Gibbs free energies (Gtilts) at pressure P=0 for 14 tilted structures of Na₃OCl relative to the Gibbs free energy for cubic (Gcubic) Na₃OCl.[이미지참조] 78
Figure 3.5. Non-equilibrium Gibbs free energies G* (T, V, P) for the (a) cubic Pm¯3m, (b) orthorhombic Bmmb, and (c) monoclinic P2₁/m, and (d) orthorhombic Pnma phases with...[이미지참조] 79
Figure 3.6. (a) Phonon band structure at various temperatures from 200 K to 500 K by considering the fourth-order anharmonic contribution. (b) Temperature dependence of the... 81
Figure 3.7. (a) Helmholtz free energy curves at various temperatures from 100 to 600 K. The minimum points at each temperature curves are marked with blue squares. (b) Thermal... 84
Figure 3.8. Band gaps for 15 phases of Na₃OCl 85
Figure 3.9. Reaction paths for Na migration are shown with the small colored spheres in (a) cubic Pm¯3m, (b) orthorhombic Bmmb, and (c) monoclinic P2₁/m phases and Na, O, and Cl... 86
Figure 4.1. Temperatures along the thermal cycle for amorphous Na₃OCl: light blue line, instantaneous T values; blue line, T values sliding average with a window of 0.1 ps. The... 92
Figure 4.2. Left: Total pair correlation functions for amorphous Na₃₋ₓOHₓCl (x=0, x=0.5, x=1) obtained at T=300 K. Right: Zoom-in into the 0.8-1.2 Å (top) and 1.8-3.2 Å (bottom) ranges. 96
Figure 4.3. Partial pair correlation functions gαβ (r) for amorphous Na₃₋ₓOHₓCl (x=0, x=0.5, x=1) at T=300 K relative to the pairs Na-O, Na-Cl, Na-Na, O-O, Cl-Cl, O-Cl, O-H, and Cl-H....[이미지참조] 98
Figure 4.4. a) Representation of the unit cell of crystalline Na₃OCl. The red polyhedra identify the octahedron O site. b) Crystalline supercell of 135 atoms (unit cell replicated 3×3x×3). c-... 99
Figure 4.5. Distributions of the structural units for Na of amorphous Na₃₋ₓOHₓCl (x=0, x=0.5, x=1) as a function of the number of neighbors in each unit (l). Values obtained by... 100
Figure 4.6. MSD versus time for each element in amorphous Na₃₋ₓOHₓCl (x=0, x=0.5, x=1)at T=300 K (top) and T=800 K (bottom). Colors legend: Na, yellow; O non-bonded... 105
Figure 4.7. a) Rotational dynamical disorder of a given H atom (grey transparent sphere) around one O atom (red opaque sphere) of one hydroxyl OH group in amorphous... 106
Figure 4.8. For the Na₂OHCl system: proton hopping process by which H atoms migrate through a dynamical switch between σ- and hydrogen-bonds giving rise to the formation of... 107
Figure 4.9. Top: Log-log plot of MSD vs time for Na in Na₃OCl at temperatures in between T=300 K and 1200 K. Bottom: corresponding values of β. Inset: β value as a function of... 111
Figure 4.10. Na-ion self-diffusion coefficients (inset) and conductivities of amorphous Na₃₋ₓOHₓCl (x=0, x=0.5, x=1). We also report the activation energies of Na ionic conduction... 112
Figure 5.1. Top: Scatter plots of DFT-computed and GAP-predicted total energies (left), forces (centre) and virials (right) for the training and testing (insets) sets of 200 configurations in total. Bottom: Cumulative error distributions: a given point (x,y) on the... 122
Figure 5.2. Total X-rays and neutrons structure factors for glassy Na₃OCl at T=300 K. The FPMD results (dark grey lines) are compared to the S T (k) in the reciprocal space (light color)... 124
Figure 5.3. Total pair correlation function for amorphous Na₃OCl at T=300 K. The FPMD results (orange black lines) are compared to the MLP calculated for GAP1 (black dashed lines)... 125
Figure 5.4. The partial pair correlation functions gNaO(r), gNaCl(r), gNaNa(r), gOO(r), gOCl(r) and gClCl(r) for amorphous Na₃OCl at T=300 K obtained from FPMD (fullfilled profiles) and...[이미지참조] 128