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A band of diffraction contrast where local bending brings a crystal structure into a particular Bragg diffraction condition. Its position changes with specimen tilt.

The orientation of a crystal structure relative to a specimen or instrument coordinate frame. It determines which Bragg diffraction conditions are excited.

For a cubic crystal, $d_{hkl}=a/\sqrt{h^2+k^2+l^2}$ and first-order bragg diffraction requires $2d_{hkl}\sin \theta =\lambda$. The face-centred lattice sum isIt is four if $h,k,l$ are all even or all odd, and zero for mixed parity. With the NaCl basis displaced by $(\frac{1}{2},0,0)$, the allowed amplitudes are $F_{hkl}=4[f_{\mathrm{Cl}}+(-1{)}^{h+k+l}{f}_{\mathrm{Na}}]$, up to the arbitrary choice of origin/species. Both allowed parity classes survive because the two ionic scattering factors are not identical. Intensities depend on $|F{|}^2$, geometry, absorption and scattering vector.

There are three separate tests: nonzero structure factor, accessible Bragg angle, and accessible plane orientation. In a symmetric reflection scan the scattering vector is normal to the specimen face, selecting the surface-parallel family and its allowed orders. Other families need a different mounting, independent orientation control or transmission/another facet. The original diagrams distinguish these geometric requirements; angles in the reciprocal-space panel are between plane normals, not Bragg angles.

Choose an objective aperture around a precipitate superlattice reflection, such as $100$, which is absent from the disordered aluminium matrix. The selected beam then makes precipitates bright in dark-field transmission electron microscopy, while the matrix gives little intensity in that beam. Tilt the grain to place the chosen reflection close to its Bragg diffraction condition and preferably approach a two-beam geometry. This reduces excitation error and can increase precipitate brightness; the exact maximum also depends on foil thickness, strain and dynamical scattering. Selecting a shared fundamental reflection would give much poorer chemical-order selectivity.

Use conventional bright-field transmission electron microscopy, with nearly parallel illumination, a suitably small objective aperture and low magnification covering the whole cross-section. More strongly scattering material sends more intensity outside the selected central beam and therefore looks darker. Tilt crystalline layers away from strong Bragg diffraction conditions to reduce diffraction contrast, and use a near-focus image so that electron phase contrast does not dominate.

The nominally uniform $150\mathrm{nm}$ thickness helps separate composition from thickness variations, but does not make the contrast purely compositional: density, atomic number and multiple scattering still matter. Choose an accelerating voltage sufficient to transmit this thickness, commonly $200$–$300\mathrm{kV}$ for a robust inorganic film, subject to its damage limit. High-angle annular dark-field imaging in scanning transmission electron microscopy is a useful alternative for approximately monotonic mass-thickness contrast, but is a different acquisition mode and still requires thickness and detector-angle control.

Diffraction contrast arises because elastic scattering transfers transmitted electron intensity between the direct beam and Bragg diffraction beams. A local change in crystal orientation, strain or thickness changes that transfer. An objective aperture selecting the direct beam makes strongly diffracting regions relatively dark in bright-field transmission electron microscopy; selecting a diffracted beam reverses the selection in dark-field transmission electron microscopy. This is a change in scattering conditions, not necessarily a change in chemical composition.

Three characteristic effects are bend contours, thickness fringes and dislocation contrast. Bend contours follow positions where a gently curved crystal meets a particular Bragg diffraction condition. Thickness fringes arise from thickness-dependent exchange of intensity between coupled transmitted and diffracted waves. A dislocation distorts nearby planes, changing their diffraction condition and producing localized contrast; changing the diffraction vector can suppress particular dislocations. Moiré fringes from overlapping lattices provide another acceptable example, but their coarse spacing is a beat spacing rather than an atomic spacing.

Use a sufficiently high SEM acceleration voltage to transmit through the particle/support combination and provide useful diffracted intensity; operation near the high-voltage end of the SEM range is a reasonable starting point. The supplied wavelength is used directly for the camera-length calculation, rather than assigning a precise voltage from an approximate wavelength relation.

Choose the smallest beam current consistent with usable counting statistics, because the stated source-size contribution obeysHigher gun brightness permits more current at the same small probe. A relatively short working distance can give a larger convergence semiangle and reduce this term. In the specified fixed lens-to-detector geometry, shortening working distance also increases the specimen-to-detector camera length, reducing the detector's collection angles.

The objective aperture should be optimized, not made arbitrarily large: increasing $\alpha$ reduces the source-size and diffraction contributions, but spherical/chromatic aberrations and angular broadening eventually worsen the probe or diffraction selectivity. A suitable aperture balances those effects while keeping the chosen diffraction rings within the annulus. Adjust specimen height to meet that angular condition, focus and align at the operating voltage, and control drift and contamination.

Low convergence favors angular discrimination of diffraction, whereas high convergence can favor probe size. The optimum therefore depends on whether spatial detail or sharply selected Bragg diffraction contrast is the limiting requirement.

For a face-centered cubic lattice, allowed reflections have indices all odd or all even. The first two are $\{111\}$ and $\{200\}$, withFor first-order Bragg diffraction, $2d\sin \theta =\lambda$. The detector intercepts the beam at the full scattering angle $2\theta$, givingThe inner detector radius supplies the minimum length for each ring:Thus both rings reach the annulus when $L\gtrsim 90.2\mathrm{mm}$. At this minimum the 200 ring is at roughly $3.12\mathrm{mm}$, well inside the $10\mathrm{mm}$ outer radius. Both remain within the detector for approximatelyEquality at the inner edge gives vanishing acceptance for an ideal infinitely narrow ring, so practical operation requires a small margin. The calculation concerns ring positions; individual nanoparticle orientation and the finite probe convergence also affect observed diffraction contrast. Using the Bragg angle instead of the full scattering angle would introduce an erroneous factor of about two.