May 3, 2020 · The reciprocal lattice definitely takes into account the basis for the Bravais Lattice. Take for example a 3-dimensional lattice with basis $\{ \vec{a}_1, \vec{a}_2, \vec{a}_3 \}$. The reciprocal basis is then. Which clearly depends on the basis vectors. Every lattice has a …

Feb 28, 2024 · Each primitive vector of the reciprocal basis must be orthogonal to $2$ of the primitive vectors of the lattice basis. And the dot product to the other must be $2\pi$ . The primitive vectors of the FCC lattice go from one of the vertices of the cube until the points at the centre of the faces (nearest neighbours).

Nov 29, 2010 · This dual lattice is extremely useful, but it is not the same thing as the fourier conjugate lattice, which is what absolutely all physicists mean by "reciprocal lattice" $\endgroup$ – wsc Commented Jan 3, 2011 at 5:05

Feb 1, 2023 · Show that point group of the reciprocal lattice is the same as the point group of the direct lattice 1 Can a point $\vec R$ in direct lattice be uniquely mapped to a point in the reciprocal space?

Nov 1, 2016 · To see this, note that this three guys belong to the reciprocal lattice, are linearly independent, and any non-entire linear combination of them doesn't belong to the reciprocal lattice. For a nice and simple introduction to solid state physics, I suggest you [2].

Feb 1, 2019 · Construct the reciprocal lattice from the standard formulas - this will also be a Bravais lattice by definition. Figure out how to draw the reciprocal space Bravais lattice with appropriate artistic touches (I'm terrible at that part). Note that the reciprocal lattice of bcc is an fcc lattice (and vice versa). $\endgroup$ –

$\begingroup$ @JonCuster I did the calculation but the basis atoms in the reciprocal space looked a bit awkward. . Their projection in xOy plane is still at the geometric center of the hexagonal grid. but as the reciprocal operation turns $\gamma=120^{\circ}$ to $\gamma '=60^{\circ}$, these atoms are in the geometric center of a 120-degree isosceles triangle, instead of the equilateral ...

Jun 22, 2017 · and these $\bar e^{k\alpha}$ vectors are our reciprocal lattice basis. Geometrically this means the reciprocal lattice vector dual to $\mathbf e_1$ is constructed by the following procedure: Find the (hyper-)plane spanned by a $\mathbf e_{2,3,\dots D}$.

Jun 22, 2016 · The reciprocal lattice is by definition its Fourier transform $\delta(\mathbf{k}-\mathbf{G})$ Now if you do the Fourier transform of the direct lattice, you will find a reciprocal lattice of side $2\pi/\mathbf{a}$.

Jun 7, 2022 · The issue is that this set of planes is not a family of lattice planes except in the special case where $\mathbf{G}$ is the smallest reciprocal lattice vector in its direction. The problem is that if $\mathbf{G}$ is not the shortest, then there are too many planes ; that is, some of the planes don't have any lattice points at all.