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15 Ιουλ 2022 · Animated example showing how to obtain the reciprocal points from a direct lattice. It should now be clear that the direct lattice, and its reticular planes, are directly associated (linked) with the reciprocal lattice.
The reciprocal lattice is constituted by the set of all possible linear combinations of the basis vectors a*, b*, c* of the reciprocal space. A point (node), H, of the reciprocal lattice is defined by its position vector: OH = rhkl* = h a* + k b* + l c*. If H is the n th node on the row OH, one has:
Definition. A reciprocal lattice is a mathematical construct used in crystallography to represent the periodicity of a crystal in momentum space rather than real space.
The reciprocal lattice. A. Authier. 1. Introduction. The fundamental property of a crystal is its triple periodicity and a crystal may be generated by repeating a certain unit of pattern through the translations of a certain lattice called the direct lattice.
The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, which is the dual of physical space considered as a vector space, and the reciprocal lattice is the sublattice of that space that is dual to the direct lattice.
Direct lattice. The reciprocal lattice of a Bravais lattice is always a Bravais lattice and has its own primitive lattice vectors, for example, b . and b 2 in the above figure. The position vector G of any point in the reciprocal lattice can be expressed in terms of the primitive lattice vectors:
Definition. The reciprocal lattice is constituted of the set of all possible linear combinations of the basis vectors a*, b*, c* of the reciprocal space. A point (node), H, of the reciprocal lattice is defined by its position vector: OH = r* hkl = h a* + k b* + l c*. If H is the nth node on the row OH, one has: OH = n OH 1 = n (h 1 a* + k 1 b ...
