Pressure and Strain Transformations in the Crystal¶

This notebook demonstrates how to use the scale_unit_cell function to apply pressure and strain transformations to a material’s unit cell, modifying its lattice parameters in various ways, including:

• Pressure-Based Scaling: Uses pressure and bulk modulus to calculate uniform strain

• UniforStrainng: Appliestrainor uniformly across all lattice directionsn.

• Anisotropic Strain: Applies strain along each lattice axis individually.

• Strain and Shear Transformations: Utilizes a strain tensor to apply anisotrotrain and sh)._

Loading a Structure¶

Crystals or molecules can be easily read from file and initiated as Structure object:

[1]:

from aim2dat.strct import Structure
strct = Structure.from_file("files/strc/Zn_MOF5_H_conv.xyz", label="Zn_MOF5_H")

Example 1: Pressure-Based Scaling¶

Applies 10 GPa pressure to strct using a bulk modulus of 1600 GPa. The resulting lattice parameters show the effect of the applied pressure.s.

[2]:

pressure_applied_structure = strct.scale_unit_cell(
    pressure= 1, # Pressure in GPa.
    bulk_modulus=16.0,  # Bulk modulus in GPa, MOF-5
    change_label=True
)

Create a pandas DataFrame to compare original and pressure-applied lattice parameters.

[3]:

import pandas as pd

pressure_lattice_comparison = pd.DataFrame({
    "Original": strct.cell,
    "Pressure Applied (10 GPa)": pressure_applied_structure.cell
}, index=["x", "y", "z"])

display(pressure_lattice_comparison)

Example 2: Uniform Strain¶

In this simpst example, we apply uniform scaling t````strct` using a scaling factor of 1.1:

• scale_unit_cell scales all lattice parameters uniformly by 1.1.

• change_label=True updates the label to reflect the transformatiation. cling.

[4]:

uniform_scaled_structure = strct.scale_unit_cell(
    scaling_factors=1.1,  # Uniform scaling factor
    change_label=True
)

Create a pandas DataFrame to compare original and scaled lattice parameters.

[5]:

lattice_comparison = pd.DataFrame({
    "Original": strct.cell,
    "Uniform Scaled (1.1)": uniform_scaled_structure.cell
}, index=["x", "y", "z"])
display(lattice_comparison)

Example 3: Anisotropic Strain¶

Applies anisotropic strain to str0] with specified strains along each axis: 2% along x, -1% along y, and 3% along z. The updated lattice parameters are printed to show the effect.

[6]:

anisotropic_strain_structure = strct.scale_unit_cell(
    scaling_factors=[1.02, 0.99, 1.03],
    change_label=True
)

Create a pandas DataFrame to compare original and anisotropically strained lattice parameters.

[7]:

anisotropic_lattice_comparison = pd.DataFrame({
    "Original": strct.cell,
    "Anisotropic Strain [1.02, 0.99, 1.03]": anisotropic_strain_structure.cell
}, index=["x", "y", "z"])

display(anisotropic_lattice_comparison)

Example 4: Anisotropic Strain and Shear Transformation¶

Applies a 3x3 strain tensor to str0], introducing both anisotropic strain and shear:

• The strain matrix specifies 2% strain along x, -1% along y, 3% along z, and shear components between x, y, and z axes.

• The scale_unit_cell function applies these transformations, and change_label=True updates the label.

The initial and transformed lattice parameters are printed to display the effects.

[8]:

strain_matrix = [
    [1.02, 0.01, 0.0],  # 2% strain along x, 0.01 shear strain between x and y.
    [0.01, 0.99, 0.0],  # -1% strain along y, 0.01 shear strain between y and x.
    [0.0, 0.02, 1.03]    # 3% strain along z, 0.02 shear strain between z and y.
]

anisotropic_strain_structure = strct.scale_unit_cell(
    scaling_factors=strain_matrix,
    change_label=True
)

Create a pandas DataFrame to compare original and strained lattice parameters.

[9]:

tensor_lattice_comparison = pd.DataFrame({
    "Original": strct.cell,
    "3x3 Strain Tensor Applied": anisotropic_strain_structure.cell
}, index=["x", "y", "z"])
display(tensor_lattice_comparison)

It is also possible to save the new structure as a .xyz file.

[10]:

anisotropic_strain_structure.to_file("files/strc/annisotropic_strain.xyz")