materials-science

Materials Science

Overview

This skill covers computational and experimental materials science: crystal structure analysis, property prediction, characterization data interpretation, and high-throughput DFT workflows. It complements the chemistry-analysis skill (which focuses on molecular systems) — this skill is for extended solids and bulk materials.

When to Use This Skill

• Analyzing crystal structures (CIF files, XRD data)
• Interpreting characterization data (XRD, SEM, TEM, XPS, AFM)
• Computing or interpreting mechanical/electronic properties from DFT
• High-throughput screening using the Materials Project database

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1. Crystal Structure

Loading and Analyzing Structures with pymatgen

from pymatgen.core import Structure, Lattice, Element
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
from pymatgen.io.cif import CifParser

# Load from CIF file
parser = CifParser("structure.cif")
structure = parser.parse_structures(primitive=True)[0]

# Basic properties
print(f"Formula: {structure.formula}")
print(f"Lattice: a={structure.lattice.a:.3f}, b={structure.lattice.b:.3f}, c={structure.lattice.c:.3f}")
print(f"Angles: α={structure.lattice.alpha:.2f}, β={structure.lattice.beta:.2f}, γ={structure.lattice.gamma:.2f}")
print(f"Volume: {structure.lattice.volume:.3f} ų")
print(f"Density: {structure.density:.3f} g/cm³")

# Symmetry analysis
sga = SpacegroupAnalyzer(structure)
print(f"Space group: {sga.get_space_group_symbol()} (#{sga.get_space_group_number()})")
print(f"Crystal system: {sga.get_crystal_system()}")
print(f"Point group: {sga.get_point_group_symbol()}")

# Get conventional standard structure
conv_structure = sga.get_conventional_standard_structure()

# Nearest neighbor analysis
for i, site in enumerate(structure.sites[:3]):
    neighbors = structure.get_neighbors(site, r=3.5)
    print(f"Site {i} ({site.specie}): {len(neighbors)} neighbors within 3.5 Å")

Miller Indices and Interplanar Spacing

import numpy as np

def bragg_d_spacing(two_theta_deg: float, wavelength_angstrom: float = 1.5406) -> float:
    """Compute d-spacing from Bragg's law: nλ = 2d sinθ (n=1)."""
    theta_rad = np.deg2rad(two_theta_deg / 2)
    return wavelength_angstrom / (2 * np.sin(theta_rad))

def bragg_two_theta(d_angstrom: float, wavelength_angstrom: float = 1.5406) -> float:
    """Compute 2θ peak position from d-spacing."""
    sin_theta = wavelength_angstrom / (2 * d_angstrom)
    if abs(sin_theta) > 1:
        return None  # no peak at this wavelength
    return 2 * np.rad2deg(np.arcsin(sin_theta))

# Example: Cu Kα radiation (λ = 1.5406 Å)
peaks = [(38.2, "Au (111)"), (44.4, "Au (200)"), (64.6, "Au (220)")]
for two_theta, label in peaks:
    d = bragg_d_spacing(two_theta)
    print(f"{label}: 2θ={two_theta}°, d={d:.3f} Å")