Merge pull request #309 from Exabyte-io/feature/SOF-7511

feature/SOF-7511 perturbation ripples graphene tutorial

lang/en/docs/tutorials/materials/specific/perturbation-ripples-graphene.md

@@ -0,0 +1,186 @@
+---
+# YAML header
+render_macros: true
+---
+
+# Ripple perturbation of a Graphene sheet.
+
+## Introduction
+
+This tutorial demonstrates the process of creating edge induced ripples in graphene nanosheet based on the work presented in the following manuscript, where the mechanical properties of graphene edges were studied.
+
+!!!note "Manuscript"
+    Thompson-Flagg, R. C., Moura, M. J. B., & Marder, M.
+    "Rippling of graphene"
+    EPL (Europhysics Letters), 85(4), 46002 (2009)
+    [DOI: 10.1209/0295-5075/85/46002](https://doi.org/10.1209/0295-5075/85/46002){:target='_blank'}.
+
+We will focus on creating graphene with edge-induced ripples that match the patterns observed in experimental studies, as shown in FIG. 1.
+
+![Rippled Graphene](/images/tutorials/materials/defects/perturbation_ripple_graphene/0-figure-from-manuscript.webp "Rippled Graphene, FIG. 1.")
+
+## 1. Create Graphene Nanoribbon
+
+### 1.1. Load Graphene Material
+
+Navigate to [Materials Designer](../../../materials-designer/overview.md) and import the graphene material from the [Standata](../../../materials-designer/header-menu/input-output/standata-import.md).
+
+![Standata Graphene Import](/images/tutorials/materials/defects/defect_creation_point_substitution_graphene/1-standata-graphene.webp "Standata Graphene Import")
+
+### 1.2. Launch JupyterLite Session
+
+Select the "Advanced > [JupyterLite Transformation](../../../materials-designer/header-menu/advanced/jupyterlite-dialog.md)" menu item to launch the JupyterLite environment.
+
+![JupyterLite Dialog](/images/jupyterlite/md-advanced-jl.webp "JupyterLite Dialog")
+
+### 1.3. Open `create_nanoribbon.ipynb` notebook
+
+Find `create_nanoribbon.ipynb` in the list of notebooks and click/double-click to open it.
+
+### 1.4. Set up nanoribbon parameters
+
+Edit notebook to set the nanoribbon parameters:
+
+```python
+# Widths and lengths are in number of unit cells
+WIDTH = 40
+VACUUM_WIDTH = 10
+LENGTH = 40
+VACUUM_LENGTH = 10
+EDGE_TYPE = "zigzag"  # "zigzag" or "armchair"
+```
+
+![Setup Nanoribbon Parameters](/images/tutorials/materials/defects/perturbation_ripple_graphene/2-jl-setup-nb-nanoribbon.webp "Setup Nanoribbon Parameters")
+
+### 1.5. Run the notebook
+
+After setting the parameters, run the notebook by selecting "Run > Run All Cells" from the menu. This will create a graphene nanoribbon with the specified dimensions.
+
+![Nanoribbon Result](/images/tutorials/materials/defects/perturbation_ripple_graphene/3-wave-result-nanoribbon.webp "Graphene Nanoribbon")
+
+## 2. Create Ripples in the Nanoribbon
+
+### 2.1. Open `create_perturbation_custom.ipynb` notebook
+
+Find `create_perturbation_custom.ipynb` in the list of notebooks and click/double-click to open it.
+
+### 2.2. Set up perturbation parameters
+
+Next, we need to set up the parameters for creating rippled graphene.
+
+Edit notebook in 1.2. to set generic perturbation parameters:
+
+```python
+# Set whether to preserve geodesic distance and scale the cell accordingly to match PBC
+PRESERVE_GEODESIC_DISTANCE = False
+
+# Set whether to use Cartesian coordinates for the perturbation function
+USE_CARTESIAN_COORDINATES = False
+MATERIAL_NAME = "Graphene"
+```
+
+Then modify section 1.3 to define the custom perturbation function:
+
+```python
+import sympy as sp
+
+# Variables for the perturbation function (for SymPy)
+variable_names = ["x", "y", "z"]
+x, y, z = sp.symbols(variable_names)
+
+# Set the parameters for the perturbation function
+AMPLITUDE = 0.09  # Ripple amplitude
+WAVELENGTH = 0.2  # Wavelength of ripples
+EDGE_WIDTH = 0.25  # Width of edge effect
+PHASE_X = 0.0  # Phase shift for x direction
+PHASE_Y = sp.pi/2  # Phase shift for y direction
+
+# Create edge masks for both x and y using polynomial functions
+left_edge_x = sp.Max(0, (EDGE_WIDTH - x) / EDGE_WIDTH)
+right_edge_x = sp.Max(0, (x - (1 - EDGE_WIDTH)) / EDGE_WIDTH)
+left_edge_y = sp.Max(0, (EDGE_WIDTH - y) / EDGE_WIDTH)
+right_edge_y = sp.Max(0, (y - (1 - EDGE_WIDTH)) / EDGE_WIDTH)
+
+# Combine edge masks
+edge_mask_x = left_edge_x + right_edge_x
+edge_mask_y = left_edge_y + right_edge_y
+edge_mask = edge_mask_x + edge_mask_y
+
+# Wave pattern
+wave_pattern = (
+    sp.sin(2 * sp.pi * x / WAVELENGTH + PHASE_X) * 
+    sp.sin(2 * sp.pi * y / WAVELENGTH + PHASE_Y)
+)
+
+# Combine waves with edge mask
+custom_sympy_function = AMPLITUDE * wave_pattern * edge_mask
+```
+
+![Setup Perturbation Function](/images/tutorials/materials/defects/perturbation_ripple_graphene/4-jl-setup-nb-final.webp "Setup Perturbation Function")
+
+Key parameters explained:
+
+- `AMPLITUDE` Controls the height of the ripples (0.09 Å)
+- `WAVELENGTH` Controls the spacing between ripples (0.2 in crystal coordinates)
+- `EDGE_WIDTH` Controls how far the ripples extend from the edges (0.25 in crystal coordinates)
+- `PHASE_X`/`PHASE_Y` Controls the phase shift of the ripple pattern
+
+### 2.3. Run the notebook
+
+After setting the parameters, run the notebook by selecting "Run > Run All Cells" from the menu.
+
+![Run All](/images/jupyterlite/run-all.webp "Run All")
+
+## 3. Pass the Material to Materials Designer
+
+The rippled graphene structure will be automatically passed back to the current Materials Designer environment where user can save it.
+
+Graphene with edge-induced ripples with amplitude of 0.09 crystal units.
+
+![Final Material](/images/tutorials/materials/defects/perturbation_ripple_graphene/5-wave-result-final.webp "Final Rippled Graphene, amplitude 0.09 crystal units")
+
+Graphene with edge-induced ripples with amplitude of 0.27 crystal units.
+
+![Final Material](/images/tutorials/materials/defects/perturbation_ripple_graphene/6-wave-result-final-2.webp "Final Rippled Graphene, amplitude 0.27 crystal units")
+
+Or user can [save or download](../../../materials-designer/header-menu/input-output.md) the material in Material JSON format or POSCAR format.
+
+## Interactive JupyterLite Notebook
+
+The following JupyterLite notebook demonstrates the process of creating rippled graphene. Select "Run" > "Run All Cells".
+
+{% with origin_url=config.extra.jupyterlite.origin_url %}
+{% with notebooks_path_root=config.extra.jupyterlite.notebooks_path_root %}
+{% with notebook_name='specific_examples/perturbation_ripple_graphene.ipynb' %}
+{% include 'jupyterlite_embed.html' %}
+{% endwith %}
+{% endwith %}
+{% endwith %}
+
+## Parameters Fine-tuning
+
+If user need to adjust the ripple pattern, user can modify these key parameters:
+
+1. To change ripple height:
+   - Adjust AMPLITUDE (higher value = taller ripples)
+
+2. To change ripple spacing:
+   - Adjust WAVELENGTH (higher value = more spread out ripples)
+
+3. To change how far ripples extend from edges:
+   - Adjust EDGE_WIDTH (higher value = ripples extend further from edges)
+
+4. To change the ripple pattern:
+   - Adjust PHASE_X and PHASE_Y to modify the wave interference pattern
+
+## References
+
+1. Thompson-Flagg, R. C., Moura, M. J. B., & Marder, M. (2009). Rippling of graphene. EPL (Europhysics Letters), 85(4), 46002. [DOI: 10.1209/0295-5075/85/46002](https://doi.org/10.1209/0295-5075/85/46002)
+
+2. A. Fasolino, J. H. Los and M. I. Katsnelson, "Intrinsic ripples in graphene," Nature Materials, 6, 858-861 (2007). [DOI: 10.1038/nmat2011](https://doi.org/10.1038/nmat2011)
+
+3. L. A. Openov & A. I. Podlivaev, "Interaction of the Stone-Wales defects in graphene", Physics of the Solid State, 52, 1, 2010. [DOI: 10.1134/S1063783415070240](https://doi.org/10.1134/S1063783415070240)
+
+## Tags
+
+`graphene`, `ripples`, `perturbation`, `2D materials`, `edge effects`, `C`

mkdocs.yml

@@ -234,6 +234,7 @@ nav:
                 - Interface between Copper and SiO2 (Cristobalite):                  tutorials/materials/specific/interface-3d-3d-copper-silicon-dioxide.md
                 - Interface between Graphene and SiO2 (alpha-quartz):                tutorials/materials/specific/interface-2d-3d-graphene-silicon-dioxide.md
                 - High-k Metal Gate Stack (Si/SiO2/HfO2/TiN):                        tutorials/materials/specific/heterostructure-silicon-silicon-dioxide-hafnium-dioxide-titanium-nitride.md
+                - Ripple perturbation of a Graphene sheet:                               tutorials/materials/specific/perturbation-ripples-graphene.md
 
 # COMMON UI COMPONENTS
     - Interface Components: