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Definition: A lattice is an infinite arrangement of points in space where the environment of any point is identical to the environment of all other points. This lattice (the real space lattice) is easily visualised in terms of the physical arrangement of molecules in the crystal.
Definition of reciprocal lattice vectors. The primitive translation vectors. The reciprocal lattice vectors, , , , represent the direct lattice. , , are defined as follows: = 2 ∙ × ×. The denominator of all three is a scalar which gives the volume of the primitive cell: = | ∙. × |.
The Reciprocal Lattice and X-Ray Diffraction. X-ray diffraction is the most commonly used method to study crystal structures. In this scheme, X-rays of wavevector k are sent into a crystal, and the scattered X-rays in the direction of a different wavevector, say k ' , are measured. k .
In reciprocal space, a reciprocal lattice is defined as the set of wavevectors of plane waves in the Fourier series of any function whose periodicity is compatible with that of an initial direct lattice in real space.
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.
Review of reciprocal lattice: Definition Consider direct lattice defined by vectors 𝑹=𝑢1 +𝑢2 +𝑢3 where 𝑢1,𝑢2,𝑢3 are integers and , , are primitive translation vectors The reciprocal lattice is defined by (primitive) vectors , , defined in the following way: =2𝜋 ×
1. Define reciprocal lattice primitive vectors b1, b2, and b3 as: 2. Relationship between real space primitive vector a and reciprocal space primitive vector b: ai⋅bj = 2πδij 3. Can generate reciprocal lattice G: G= l b1 + m b2 + n b3 (l, m, n are any ingtegers) 4. In general, the longer is a, the shorter is b. That’s why b is called the ...
