Nanoscale Characterisation Techniques

Seeing and measuring the invisible. Learn electron microscopy (SEM, TEM, HRTEM, STEM, EDS), scanning probe microscopy (AFM, STM), X-ray diffraction with Bragg's law and Scherrer crystallite size, dynamic light scattering and zeta potential, UV-Vis and photoluminescence spectroscopy, Raman (graphene layers), XPS surface chemistry, BET surface area, and choosing the right technique — with Python for d-spacing, Scherrer size, DLS hydrodynamic diameter and the electron wavelength that sets TEM resolution.

Visible light can't resolve features smaller than ~200 nm, so nanotechnology relies on electrons, X-rays, scanning tips and spectroscopies to see size, shape, structure and chemistry.

Each technique measures something different — a TEM image, an XRD peak width and a DLS size of the same sample can legitimately disagree, and understanding why is essential.

An analogy

Characterising nanomaterials is like identifying a suspect with several witnesses: the TEM sees their face, XRD reads their fingerprints (crystal structure), DLS sees how they move in a crowd, and XPS checks what they're wearing on the surface.

Microscopy

Imaging techniques:

• SEM — scanned electron beam; surface morphology, ~1–5 nm resolution; EDS for elements
• TEM/HRTEM — electrons through thin samples; lattice fringes, sub-Å resolution with aberration correction
• STEM-HAADF — atomic-number contrast imaging, single atoms
• AFM — sharp tip scans surface; 3D topography, works in air/liquid, mechanical properties
• STM — tunnelling current; atomic resolution on conductive surfaces

Diffraction and scattering

XRD identifies crystal phases (compare with ICDD database), lattice parameters (Bragg), crystallite size (Scherrer — valid below ~100 nm, ignoring strain) and strain (Williamson–Hall). SAXS measures size distributions of particles in solution. DLS measures Brownian diffusion to give hydrodynamic size; zeta potential indicates colloidal stability (|ζ| > 30 mV usually stable).

Spectroscopy and surface analysis

UV-Vis absorption (plasmon peaks, quantum-dot band edges), photoluminescence (emission, quantum yield), Raman (graphene G/2D bands reveal layer number and defects via D band), FTIR (surface ligands), XPS (surface elemental and chemical state, top ~5–10 nm), BET nitrogen adsorption (specific surface area and porosity), TGA (ligand content), ICP-MS (composition and concentration).

Choosing and combining techniques

Different techniques weight sizes differently: TEM gives number-weighted core size, DLS intensity-weighted hydrodynamic size, XRD volume-weighted crystallite size — a particle can be polycrystalline, so Scherrer size < TEM size. Use complementary techniques, report statistics (count > 200 particles in TEM), and consider sample preparation artefacts (drying aggregation, beam damage). In-situ and cryo-EM methods capture dynamics and soft materials.

Formulas

• Bragg's law: nλ = 2d·sin θ
• Scherrer equation: D = Kλ/(β cos θ), K ≈ 0.9
• Stokes–Einstein (DLS): d_H = kT/(3πηD_t)
• Electron wavelength (relativistic): λ = h/√(2m₀eV(1 + eV/2m₀c²))
• Abbe limit (light): d = λ/(2NA)

Worked example: Bragg spacing

Given: λ 0.154 nm, 2θ = 44.4°

Find: d.

• 0.154/(2 sin 22.2°)

Answer: 0.204 nm (Au 200)

Worked example: Scherrer

Given: FWHM 0.5° at 2θ = 38.2°

Find: D.

• 0.1387/(0.00873 × 0.945)

Answer: 16.8 nm

Worked example: DLS

Given: D_t = 2 × 10⁻¹¹ m²/s in water

Find: d_H.

• Half of D_t → double size

Answer: 24.5 nm

XRD, DLS and electron wavelength

import math
# XRD: Bragg spacing and Scherrer crystallite size; DLS: Stokes-Einstein hydrodynamic diameter
lam = 0.15406                               # Cu K-alpha (nm)
two_theta, fwhm_deg = 38.2, 0.9             # Au (111) peak
theta = math.radians(two_theta / 2)
d = lam / (2 * math.sin(theta))
beta = math.radians(fwhm_deg)
D = 0.9 * lam / (beta * math.cos(theta))
print(f"d-spacing {d:.4f} nm, Scherrer crystallite size {D:.1f} nm")
kB, T, eta = 1.381e-23, 298.15, 0.00089     # water viscosity Pa.s
Dt = 4.0e-11                                 # diffusion coefficient m2/s from DLS
dh = kB * T / (3 * math.pi * eta * Dt)
print(f"hydrodynamic diameter {dh*1e9:.1f} nm")
# SEM/TEM resolution limit set by electron wavelength at 200 kV (relativistic)
V = 200e3
lam_e = 6.626e-34 / math.sqrt(2 * 9.109e-31 * 1.602e-19 * V * (1 + 1.602e-19 * V / (2 * 9.109e-31 * 9e16)))
print(f"electron wavelength at 200 kV = {lam_e*1e12:.2f} pm")
# d-spacing 0.2354 nm, Scherrer crystallite size 9.3 nm
# hydrodynamic diameter 12.3 nm
# electron wavelength at 200 kV = 2.51 pm

The Au(111) peak gives the expected 0.235 nm spacing, and its broadening indicates ~9 nm crystallites. DLS reports 12.3 nm — larger because it includes the ligand shell and solvation layer, and is intensity-weighted toward bigger particles. 200 kV electrons have a 2.5 pm wavelength, so TEM resolution (~0.05–0.2 nm) is limited by lens aberrations, not wavelength.

Common mistakes

• Wrong: Expecting DLS and TEM sizes to agree. — Right: DLS includes shell/solvation and is intensity-weighted.
• Wrong: Using Scherrer for > 100 nm or strained crystals. — Right: Account for instrument broadening and strain.
• Wrong: Measuring a few TEM particles. — Right: Count hundreds for meaningful statistics.

Applications

• Semiconductor metrology: CD-SEM, TEM cross-sections of transistors.
• Nanomedicine QC: DLS size and zeta for lipid nanoparticles.
• Catalyst development: STEM, XPS, BET.
• Graphene quality: Raman layer counting.

Key takeaways

• Electrons and probes image below optical limits.
• Bragg for spacing; Scherrer for crystallite size.
• DLS gives hydrodynamic size and zeta stability.
• Combine techniques — each weights size differently.

Going further

• Aberration-corrected STEM: Atom-by-atom imaging and EELS.
• Cryo-EM: Structures of lipid nanoparticles and proteins.
• In-situ liquid-cell TEM: Watching nucleation and growth.