X-Ray Diffraction for Nanomaterials: Phase Analysis, Crystal Structure, and Size Determination

What X-Ray Diffraction Tells You

X-ray diffraction (XRD) — more precisely, powder X-ray diffraction (PXRD) as routinely used for nanomaterials — is a bulk technique that interrogates millions of crystallites simultaneously and yields phase-averaged structural information. Unlike TEM, which images individual particles, XRD gives you the collective crystallographic answer for your whole sample: what phase it is, what the lattice parameters are, how large the crystalline domains are, and how much of the material is crystalline vs amorphous.

For nanomaterials, XRD adds a critical insight that bulk characterisation cannot provide: diffraction peaks broaden as crystallite size decreases. A 5 nm iron oxide nanoparticle produces noticeably broader XRD peaks than a 50 nm particle of the same material, and quantitative analysis (the Scherrer equation) extracts the crystallite size from this broadening. This makes XRD a fast, non-destructive size measurement tool complementary to TEM.

The Principles of X-Ray Diffraction

When a monochromatic X-ray beam of wavelength λ hits a crystalline sample, atoms in the crystal planes scatter the X-rays. Constructive interference occurs only when the Bragg condition is satisfied:

nλ = 2d sin θ

Where n is an integer (order of diffraction), d is the spacing between parallel crystal planes (d-spacing or d value), and θ is the angle between the incident beam and the crystal planes.

For a powder sample (many randomly oriented crystallites), some crystallites will always be oriented to satisfy Bragg's law for each set of planes. The result is a diffraction pattern of peaks at characteristic 2θ angles — a fingerprint of the crystal structure that can be matched against reference databases.

Standard XRD Instruments

Laboratory Powder Diffractometers

The workhorse instrument for nanomaterial characterisation is the Bragg-Brentano diffractometer, typically using:

• X-ray source — sealed X-ray tube with copper anode emitting CuKα radiation at λ = 0.15406 nm. Some applications use cobalt (λ = 0.17902 nm) to avoid iron fluorescence, or molybdenum (λ = 0.07107 nm) for better penetration of dense materials.
• Goniometer — mechanically scans both the X-ray tube (or detector) through the angular range 2θ = 5° to 90°+ while the sample sits flat or rotates.
• Detector — older instruments use scintillation detectors (point detectors). Modern instruments use position-sensitive detectors (VANTEC, X'Celerator, LynxEye) that collect a range of 2θ simultaneously, reducing measurement time from hours to minutes.
• Monochromator or Kβ filter — removes Kβ radiation to keep the beam monochromatic.

Synchrotron XRD

Synchrotron facilities (Diamond Light Source, European Synchrotron Radiation Facility, APS) provide X-ray beams with intensity 10⁸–10¹² times brighter than laboratory sources, tunable wavelength, and high collimation. Synchrotron XRD enables:

• Characterisation of very small sample quantities (submilligram)
• Pair distribution function (PDF) analysis for amorphous or nanocrystalline materials
• In-situ and operando experiments (reaction monitoring, temperature series)
• High-angular-resolution measurements that separate overlapping reflections
• Total scattering experiments for short-range structure in disordered materials

Grazing Incidence XRD (GIXRD)

For thin films and surface coatings, a grazing incidence geometry (X-ray beam at 0.1–5° to the surface) dramatically increases the path length through the film while minimising signal from the substrate. GIXRD characterises the phase, crystallinity, and texture of nanostructured films (TiO₂ photocatalytic coatings, ZnO thin films, ALD-deposited layers) without substrate interference.

Reading an XRD Pattern

An XRD pattern plots diffracted intensity vs 2θ (twice the Bragg angle). Key features:

• Peak positions — the 2θ values at which diffraction peaks occur are characteristic of the crystal structure and lattice parameters. Each material has a unique set of peak positions — its "fingerprint."
• Peak intensities — relative intensities depend on which atoms occupy which positions and their scattering power. The intensity pattern is used to distinguish polymorphs (e.g. anatase vs rutile TiO₂ have different intensity ratios) and to quantify phase mixtures.
• Peak widths — broadening due to small crystallite size and/or lattice strain. The key parameter for nanomaterial sizing.
• Background — amorphous materials scatter diffusely without sharp peaks, contributing a broad "hump" to the background. A large amorphous background with weak peaks indicates low crystallinity.

Phase Identification Using ICDD/JCPDS Database

The International Centre for Diffraction Data (ICDD) maintains the Powder Diffraction File (PDF) database — over 900,000 reference patterns for crystalline materials. Every diffractometer software package (HighScore, Match!, MDI JADE, EVA) can automatically compare your measured pattern against the PDF database and identify matching phases. This is straightforward for known materials but requires care for:

• Nanomaterials with broad peaks (systematic Scherrer broadening shifts apparent peak positions)
• Heavily strained materials
• Mixtures of phases with overlapping peaks
• Non-stoichiometric or doped compounds with shifted lattice parameters

The Scherrer Equation: Crystallite Size from Peak Width

The most widely used application of XRD in nanomaterials characterisation is crystallite size determination via the Scherrer equation:

D = Kλ / (β cos θ)

Where D is the volume-weighted mean crystallite dimension, K is the Scherrer shape factor (typically 0.9 for approximately spherical crystallites), λ is the X-ray wavelength, β is the peak full-width at half-maximum (FWHM) in radians after correcting for instrumental broadening, and θ is the Bragg angle.

Important nuances:

• Scherrer gives the coherent scattering domain size, not the physical particle size. A single 20 nm particle may contain multiple crystalline domains of 5 nm — Scherrer gives 5 nm.
• Always subtract instrumental peak broadening (measured from a standard sample like LaB₆ NIST SRM 660) before applying Scherrer.
• Use FWHM from a Pseudo-Voigt or Lorentzian peak fit, not just visual peak width.
• The equation is most reliable for crystallites < 100 nm. Above this, peak broadening becomes too small to measure accurately with laboratory XRD.
• Lattice strain (from defects, surface stress, compositional variations) also broadens peaks. Use the Williamson-Hall plot (β cos θ vs sin θ) to separate size broadening from strain broadening.

Rietveld Refinement

Full-pattern fitting by Rietveld refinement models the entire diffraction pattern (peak positions, widths, intensities, background) based on the crystal structure and instrumental parameters, then refines the structural model to minimise the difference between calculated and measured patterns. Rietveld provides:

• Accurate lattice parameters (to 4–5 significant figures)
• Quantitative phase analysis (weight fractions of multiple phases in a mixture)
• Crystallite size and microstrain from peak shape refinement
• Atomic positions, site occupancies, and atomic displacement parameters for complete structure solution

Rietveld refinement software: TOPAS (Bruker), FullProf, MAUD (free), Jana2020.

XRD for Common Nanomaterial Systems

Iron Oxide Nanoparticles (Fe₃O₄ / γ-Fe₂O₃)

Magnetite (Fe₃O₄) and maghemite (γ-Fe₂O₃) are both cubic spinel structures with very similar lattice parameters (0.8396 nm vs 0.8346 nm respectively). The XRD patterns are nearly identical — the small lattice parameter difference is difficult to distinguish in broad nanomaterial peaks. Rietveld refinement of high-quality patterns or synchrotron data is needed for definitive differentiation. The (311) and (440) reflections around 2θ = 35° and 63° (CuKα) are the strongest markers.

TiO₂ Nanoparticles

TiO₂ occurs in three main phases: anatase (tetragonal, photocatalytically active), rutile (tetragonal, thermodynamically stable, lower photocatalytic activity), and brookite (orthorhombic, rare). XRD clearly distinguishes these because their peak patterns differ substantially. The anatase (101) peak at 2θ ≈ 25.3° and the rutile (110) peak at 2θ ≈ 27.4° (CuKα) are the diagnostic markers. Quantitative Rietveld analysis gives anatase:rutile ratios in mixed-phase samples like Evonik P25.

Graphene and Graphene Oxide

Graphite shows a sharp (002) peak at 2θ ≈ 26.5° (CuKα), corresponding to an interlayer d-spacing of 0.335 nm. Oxidation expands this spacing: GO shows a broad (001) peak at 2θ ≈ 10–12° (d-spacing 0.7–0.9 nm depending on oxidation degree and hydration). Reduced graphene oxide (rGO) shows a broad peak shifting back towards 2θ ≈ 24–26°, confirming restoration of the graphitic structure. The breadth of the rGO peak reflects the small, disordered graphitic domain sizes.

Quantum Dots (CdSe, InP)

CdSe quantum dots crystallise in the zinc blende or wurtzite structure depending on synthesis conditions. XRD confirms the crystal phase and provides Scherrer crystallite sizes consistent with TEM measurements. The broad, diffuse peaks of very small QDs (2–5 nm) require careful fitting and Scherrer correction. InP QDs similarly show the zinc blende InP diffraction pattern with Scherrer broadening.

Sample Preparation for XRD

• Powder samples — grind to a fine, homogeneous powder. Pack into a flat sample holder or zero-background silicon holder to minimise preferred orientation and background. Sample height critically affects peak positions — use a height gauge.
• Nanoparticle dispersions — centrifuge or vacuum-filter to collect the powder; dry thoroughly under vacuum. Residual solvent or surface ligands may contribute background features.
• Films — use GIXRD geometry. Ensure the substrate contribution is characterised separately for subtraction if needed.
• Sample amount — typically 50–200 mg for standard analysis; as little as 5 mg is feasible with thin-film holders and modern position-sensitive detectors.