Reciprocal vectors are defined to be perpendicular to two of the three lattice
vectors and with length equal to 1/length of the third vector.
Linear combinations formed from these reciprocal vectors and the
Miller indices are vectors that are in the same direction as the poles to
the corresponding planes. The vector length of this vector is the
reciprocal of the plane spacing.
genneth said:If you're familiar with vector spaces and their duals, let [tex]\mathbf{e}_\mu[/tex] be the basis vectors for V, and [tex]\mathbf{\theta}^\mu[/tex] be the (co-)basis for V*, such that [tex]\mathbf{e}_\mu \mathbf{\theta}^\nu = \delta_\mu^\nu.[/tex] Let there be a metric, [tex]g_{\mu\nu}.[/tex] The reciprocal vectors are basis covectors [tex]\mathbf{\theta}^\mu[/tex] turned into vectors by the inverse metric.
malawi_glenn said:Thanx , but not what I looked for ;)
genneth said:I know it sounds a bit esoteric, but it's really just geometry. I certainly didn't understand reciprocal lattice vectors until I made that connection -- but maybe I'm just a mathmo trying to pretend to be a physicist ;-)
malawi_glenn said:The geometrical connetion I am fine with, but I am after the physical intepretation of the reciprocal lattice vector.
I know that the answer to this: "So I wonder if the points in reciprocal space represent allowed k-values for waves that can be Bragg-difracted in the real-lattice. And if the reciprocal lattice vector represent a certain k-value."
Is that the allowed k-vales are contained in the 1BZ, so I now wonder what points in reciporcal lattice space and reciprocal lattice vectors represents. If there are any physical inteprenation of those, or just geometrical.
malawi_glenn said:Homework Statement
"What does a reciprocal lattice vector represent in the real lattice?"
Kurdt said:Think about the change in wavevector of incident radiation upon a lattice.
malawi_glenn said:You are talking about Bragg condition right?
Kurdt said:I am indeed. Now to help you a little more, consider a 1D lattice with an incident wavevector k and a reflected wavevector k'. Take the difference of the wavevectors and see if they look familiar.
Reciprocal lattice vectors are a set of vectors that define the periodicity of a crystal lattice in reciprocal space. They are used to describe the diffraction of a crystal lattice in X-ray crystallography.
Reciprocal lattice vectors are mathematically related to real space lattice vectors through the reciprocal lattice transformation. This transformation is used to convert between real space and reciprocal space representations of the crystal lattice.
Reciprocal lattice vectors are calculated by taking the cross product of two basis vectors of the real space lattice and then taking the inverse of the resulting vector. This process is repeated for each basis vector of the real space lattice to obtain the full set of reciprocal lattice vectors.
Reciprocal lattice vectors are essential in crystallography as they provide a way to describe the periodicity and symmetry of a crystal lattice. They also play a crucial role in analyzing the diffraction patterns of crystals, which are used to determine the structure of a crystal.
The reciprocal lattice vectors determine the spacing and intensity of the diffraction spots in a crystal's diffraction pattern. They also help in identifying the crystal system and lattice parameters of a crystal through the analysis of the diffraction pattern.