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Concept
Zone axis
Résumé
Zone axis, a term sometimes used to refer to "high-symmetry" orientations in a crystal, most generally refers to any direction referenced to the direct lattice (as distinct from the reciprocal lattice) of a crystal in three dimensions. It is therefore indexed with direct lattice indices, instead of with Miller indices.
High-symmetry zone axes through a crystal lattice, in particular, often lie in the direction of tunnels through the crystal between planes of atoms. This is because, as we see below, such zone axis directions generally lie within more than one plane of atoms in the crystal.
Miller index
The translational invariance of a crystal lattice is described by a set of unit cell, direct lattice basis vectors (contravariant or polar) called a, b, and c, or equivalently by the lattice parameters, i.e. the magnitudes of the vectors, called a, b and c, and the angles between them, called α (between b and c), β (between c and a), and γ (between a and b). Direct lattice vectors have components measured in distance units, like meters (m) or angstroms (Å).
A lattice vector is indexed by its coordinates in the direct lattice basis system and is generally placed between square brackets []. Thus a direct lattice vector , or , is defined as . Angle brackets 〈〉 are used to refer to a symmetrically equivalent class of lattice vectors (i.e. the set of vectors generated by an action of the lattice's symmetry group). In the case of a cubic lattice, for instance, 〈100〉 represents [100], [010], [001], [00], [00] and [00] because each of these vectors is symmetrically equivalent under a 90 degree rotation along an axis. A bar over a coordinate is equivalent to a negative sign (e.g., ).
The term "zone axis" more specifically refers to the direction of a direct-space lattice vector. For example, since the [120] and [240] lattice vectors are parallel, their orientations both correspond the 〈120〉 zone of the crystal.
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Concepts associés (7)
Zone axis
Zone axis, a term sometimes used to refer to "high-symmetry" orientations in a crystal, most generally refers to any direction referenced to the direct lattice (as distinct from the reciprocal lattice) of a crystal in three dimensions. It is therefore indexed with direct lattice indices, instead of with Miller indices. High-symmetry zone axes through a crystal lattice, in particular, often lie in the direction of tunnels through the crystal between planes of atoms.
Precession electron diffraction
Precession electron diffraction (PED) is a specialized method to collect electron diffraction patterns in a transmission electron microscope (TEM). By rotating (precessing) a tilted incident electron beam around the central axis of the microscope, a PED pattern is formed by integration over a collection of diffraction conditions. This produces a quasi-kinematical diffraction pattern that is more suitable as input into direct methods algorithms to determine the crystal structure of the sample.
Réseau réciproque
En cristallographie, le réseau réciproque d'un réseau de Bravais est l'ensemble des vecteurs tels que : pour tous les vecteurs position du réseau de Bravais. Ce réseau réciproque est lui-même un réseau de Bravais, et son réseau réciproque est le réseau de Bravais de départ. Un cristal peut se décrire comme un réseau aux nœuds duquel se trouvent des motifs : atome, ion, molécule. Si l'on appelle les vecteurs définissant la maille élémentaire, ces vecteurs définissent une base de l'espace.
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Learn about the fundamentals of transmission electron microscopy in materials sciences: you will be able to understand papers where TEM has been used and have the necessary theoretical basis for takin
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