Drawing a reciprocal lattice, also basis

In summary, The conversation discusses drawing a reciprocal lattice and calculating the bases vectors of different types of lattices. It is mentioned that any lattice can be spanned by only 3 lattice vectors and the concept of a "primitive cell" is brought up. The correct notation for reciprocal lattice vectors is also discussed.
  • #1
thegirl
41
1
Hey could anyone please explain how you go about drawing a reciprocal lattice? For example a 2d rectangular lattice to it's reciprocal form?

Also... I don't know if this is correct but if you have a 2d rectangular lattice with lattice vectors L=n1a1 + n2a2

would the reciprocal lattice vectors be G = h(2pi/a1) + k (2pi/a2) ?

Another question I have is why do fcc's have 4 bases whereas a bcc only has 2? How would you go about calculating the bases vectors of any lattice?
 
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  • #2
thegirl said:
Another question I have is why do fcc's have 4 bases whereas a bcc only has 2? How would you go about calculating the bases vectors of any lattice?

I think any lattice can be spanned by only 3 (in 2-D 2) lattice vectors, independently whether the lattice is centered or not. Look for "primitive cell".
 
  • #3
thegirl said:
Heycould anyone please explain how you go about drawing a reciprocal lattice? For example a 2d rectangular lattice to it's reciprocal form?

Also... I don't know if this is correct but if you have a 2d rectangular lattice with lattice vectors L=n1a1 + n2a2

would the reciprocal lattice vectors be G = h(2pi/a1) + k (2pi/a2) ?
I think you are basically right, but you should be careful about vector notation. I.e. if a1 is a vector, then you can't form (2pi/a1).
 

1. What is a reciprocal lattice?

A reciprocal lattice is a mathematical construct used in crystallography to describe the periodicity of a crystal structure. It is the Fourier transform of the direct lattice, and is often represented as a set of points in reciprocal space.

2. How is a reciprocal lattice drawn?

A reciprocal lattice is typically drawn using a graphical method known as the Ewald construction. This involves drawing a set of reciprocal lattice points that correspond to the direct lattice points, and connecting them to form a lattice of reciprocal vectors.

3. What is the basis of a reciprocal lattice?

The basis of a reciprocal lattice is a set of primitive vectors that define the unit cell in reciprocal space. These vectors are perpendicular to the reciprocal lattice vectors, and their lengths are inversely proportional to the lengths of the corresponding direct lattice vectors.

4. Why is the basis important in drawing a reciprocal lattice?

The basis is important because it allows us to define the orientation and scale of the reciprocal lattice. By choosing different basis vectors, we can draw the reciprocal lattice in different orientations or with different spacing between reciprocal lattice points.

5. What is the relationship between the direct lattice and the reciprocal lattice?

The direct lattice and the reciprocal lattice are related by the equation G = 2πH, where G is a reciprocal lattice vector and H is a direct lattice vector. This relationship allows us to calculate the reciprocal lattice vectors from the direct lattice vectors, and vice versa.

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