The five ring p orbitals form one nondegenerate and two doubly degenerate symmetry-adapted sets. About the ring normal, these match metal $d_{z^2}$, $(d_{xz},d_{yz})$, and $(d_{xy},d_{x^2-y^2})$ by sigma, pi and delta symmetry respectively. Matching symmetry permits interaction, but spatial overlap and energy separation determine its strength.

A puckered conformation with an approximately planar alkene end and a nonplanar saturated part. Bulky substituents commonly favor pseudoequatorial positions.

The five-membered cyclic anhydride of cis-butenedioic acid.

A crystal system classifies crystals by their point-symmetry properties. The conventional three-dimensional classification has seven systems: triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic.

This is distinct from counting the fourteen Bravais lattices, which also distinguish allowed lattice centerings. A unit-cell drawing gives a convenient coordinate description, but symmetry, rather than merely an arbitrary choice of cell lengths, determines the crystal system.

Wavelength-dependent complex atomic scattering, written $f=f_0+f^{\prime }+i{f}^{\prime \prime }$. Its imaginary component can break equality of Friedel-pair intensities.

The reflections with reciprocal indices $\mathbf{h}$ and $-\mathbf{h}$. Their amplitudes are complex conjugates for a real scattering density, but anomalous scattering can make their intensities unequal.

The Fourier transform of diffraction intensities. Its peaks give weighted interatomic displacement vectors; a common translation of the atomic structure is invisible.

The complete group of spatial symmetry operations of a periodic crystal, including translations and combinations such as screw axes and glide planes.

A strong-reflection inference in a centrosymmetric structure: $S(h{)}^{2}S(2h)\simeq +1$, favoring positive $F(2h)$. It depends on positivity and concentrated atomic density, rather than holding for every weak Fourier coefficient.

For suitable strong reflections, phases tend to satisfy ${\varphi }_h+{\varphi }_k-{\varphi }_{h+k}\simeq 0$. In a centrosymmetric origin this becomes $S(h)S(k)S(h+k)\simeq +1$. The phase combination is origin invariant.

The spatial transformations that preserve a crystal structure.

Diffraction from a specimen containing many crystallite orientations. Equivalent reciprocal-lattice spacings produce powder rings or corresponding peaks in an angular scan. Powder diffraction multiplicity counts the equivalent directed normals contributing to a reflection family.

A line defect in a crystal structure. Its Burgers vector measures the closure failure of a circuit around the line. Motion can produce permanent plasticity without simultaneously breaking every bond across a whole plane.

A bond rotation that changes four hexagons in a graphitic carbon network into a pentagon-heptagon-heptagon-pentagon ring arrangement without adding or removing atoms.

A missing carbon atom or group of atoms in a carbon nanotube wall. Local reconstruction can produce a 5–9 monovacancy or 5–8–5 divacancy ring inventory; larger vacancies can interrupt a shell.

Notation specifying a defect species, its lattice site and its charge relative to the corresponding ideal lattice site.

A localized crystal defect such as a vacancy, substitutional impurity or interstitial atom.

An interface between crystalline regions with different orientations. Its structure affects transport, mechanical response and absorption of mobile point defects.

An interface between ordered domains related by a displacement that is a translation of the underlying disordered lattice but not of the ordered chemical structure. Slip by that displacement can leave an antiphase boundary behind a dislocation; a second appropriate displacement can restore the order.

A finite particle composed of several crystallographically twinned domains. A composite fivefold outline does not require one periodic lattice to have fivefold rotational symmetry. In a decahedral fcc model, five tetrahedral domains meet around a common near-$⟨110⟩$ axis; elastic distortion accommodates the angular deficit.