An analytical method that shines X-rays on a crystal and uses the angles and intensities of the diffracted X-rays to examine crystalline phases, lattice parameters, crystallite size, strain, texture and more.
Japanese name: XRD(X線回折)
XRD (X-ray diffraction) appears in 9 practice questions across 5 topics, including Materials characterization (SEM, TEM, XRD, XPS), Crystal structures and Miller indices, Polymers and composites.
XRD shines X-rays on a crystal, whose atomic spacings are comparable to the X-ray wavelength, and measures the diffracted X-rays that reinforce at angles satisfying Bragg's law. Peak positions give interplanar spacings and lattice parameters, and comparing the pattern with a database identifies the crystalline phases. Peak intensity ratios reveal texture and phase proportions, and peak widths reveal crystallite size and nonuniform strain. Amorphous materials show a broad halo instead of peaks, so XRD can also tell whether a material is crystalline or amorphous.
For powders and polycrystalline specimens, the basic method is θ-2θ measurement (Bragg–Brentano focusing), in which the specimen and detector rotate in step. In this geometry only planes parallel to the specimen surface are seen. For thin films, grazing-incidence measurements that send X-rays in at a shallow angle to probe only the near-surface region, rocking curves for examining texture and lattice tilt, and reciprocal space maps for examining the composition and strain of epitaxial films are used. Cu Kα radiation (wavelength about 0.154 nm) is the most commonly used X-ray source.
Precise lattice parameters obtained from peak positions allow estimates of solid-solution composition (Vegard's law) and residual stress (the sin²ψ method). Proportions of multiple phases are found by comparing peak intensities with standards or by Rietveld analysis, which fits the entire pattern to a calculation. Peak widths give crystallite size through the Scherrer equation, but instrumental broadening must be subtracted and the strain contribution separated. Accurate results require angle calibration and correction for specimen height displacement.
In process work, XRD is used to confirm the phase and texture of deposited films (for example, identifying silicide phases or the (111) texture of Cu interconnects), to confirm crystallization by heat treatment, and to identify corrosion products and foreign matter. Detection generally requires a content of several percent or more and a certain volume, however, so XRD is poor at detecting tiny particles or trace phases. In such cases it is combined with micro-area XRD, electron diffraction in TEM, Raman spectroscopy and the like. A major advantage is that it is nondestructive, so it can be performed before other analyses.
Answer: B. About 28.4°
From Bragg's law 2d sinθ = nλ (n = 1), sinθ = 0.15406/(2 × 0.3135) ≈ 0.2457, so θ ≈ 14.2° and the diffraction angle is 2θ ≈ 28.4°. XRD instruments and data normally plot 2θ, the angle between the incident and diffracted X-rays, on the horizontal axis. About 14.2° is the mistake of answering θ itself, and about 58.9° drops the 2 in Bragg's equation and uses sinθ = λ/d. The peak of silicon powder near 28.4° is strong and sharp, so it is also widely used as a standard for calibrating diffraction angles.
Answer: C. (111)
In FCC, diffraction appears only when h, k and l are all even or all odd; when even and odd are mixed, the scattering from the four atoms in the unit cell cancels and the intensity is zero (the extinction rules). Peaks therefore appear in the order (111), (200), (220), (311)…, and (111), with the smallest h² + k² + l², has the largest interplanar spacing and the lowest angle. (100) and (110) both mix even and odd indices and so do not appear in FCC. In BCC only planes with h + k + l even appear, so the first peak is (110), and the sequence of peaks distinguishes FCC from BCC.
XRD reveals crystal structure and cannot directly measure which elements are present. It can distinguish phases of the same elements with different structures, but elemental analysis calls for combining it with EDS, X-ray fluorescence or similar techniques.
No sharp peaks appear, only a broad, gentle hump (a halo). If peaks appear after heat treatment, you can conclude that the film has crystallized.
It depends on the material and the incidence angle, but in θ-2θ measurement it reaches several to several tens of micrometers in metals, and deeper still in materials of light elements. To measure only a thin film, use a grazing-incidence geometry.
XRD instruments and data normally plot 2θ, the angle between the incident and diffracted X-rays, on the horizontal axis.
In XRD with Cu Kα radiation (wavelength 0.15406 nm), which …The spacing gets smaller as the indices get larger, and in XRD, planes with smaller d diffract at higher angles.
Which value is closest to the interplanar spacing of the (1…The density method is a simple way to measure crystallinity; it can also be obtained from the heat of fusion by DSC or the ratio of crystalline peak areas in X-ray diffraction.
Take the density of perfectly crystalline polyethylene as 1…XRD examines crystal structure and lattice parameters and cannot measure concentration profiles of trace elements.
In semiconductor failure analysis, which technique is best …What XRD peak widths give is the crystallite size by the Scherrer equation, not the surface area of the particles themselves.
Which correctly describes the principle of the BET method f…Bragg's law Extinction rules Scherrer equation Crystallinity SIMS (secondary ion mass spectrometry) EDS (energy-dispersive X-ray spectroscopy) BET method Specific surface area SEM (scanning electron microscope) XPS (X-ray photoelectron spectroscopy)