In physics, the Bragg plane is the plane in reciprocal space which bisects the reciprocal lattice vector . It is relevant to define this plane as part of the definition of the Von Laue condition for diffraction peaks in x-ray diffraction crystallography.
Considering the diagram at right, the arriving x-ray plane wave is defined by:
Where is the incident wave vector given by:
where is the wavelength of the incident photon. While the Bragg formulation assumes a unique choice of direct lattice planes and specular reflection of the incident X-rays, the Von Laue formula only assumes monochromatic light and that each scattering center acts as a source of secondary wavelets as described by the Huygens principle. Each scattered wave contributes to a new plane wave given by:
The condition for constructive interference in the direction is that the path difference between the photons is an integer multiple (m) of their wavelength. We know then that for constructive interference we have:
where . Multiplying the above by we formulate the condition in terms of the wave vectors and :
Now consider that a crystal is an array of scatterering centres, each at a point in the Bravais lattice. We can set one of the scattering centres as the origin of an array. Since the lattice points are displaced by the Bravais lattive vectors, scattered waves interfere constructively when the above condition holds simultaneously for all values of which are Bravais lattice vectors, the condition then becomes:
An equivalent statement (see mathematical description of the reciprocal lattice) is to say that:
By comparing this equation with the definition of a reciprocal lattice vector, we see that constructive interference occurs if is a vector of the reciprocal lattice. We notice that and have the same magnitude, we can restate the Von Laue formulation as requiring that the tip of incident wave vector must lie in the plane that is a perpendicular bisector of the reciprocal lattice vector . This reciprocal space plane is the Bragg plane.
Famous quotes containing the words bragg and/or plane:
“There’s nothing the British like better than a bloke who comes from nowhere, makes it, and then gets clobbered.”
—Melvyn Bragg (b. 1939)
“At the moment when a man openly makes known his difference of opinion from a well-known party leader, the whole world thinks that he must be angry with the latter. Sometimes, however, he is just on the point of ceasing to be angry with him. He ventures to put himself on the same plane as his opponent, and is free from the tortures of suppressed envy.”
—Friedrich Nietzsche (1844–1900)